Impact Factor: 0.9

Zeitschrift

Forum Mathematicum

Editor-in-Chief: Guozhen Lu
Wissenschaftlicher Beirat: Thomas Alazard , Jan Hendrik Bruinier , Manfred Droste , Siegfried Echterhoff , Maria del Mar Gonzalez , Philipp Habegger , Matthias Hieber , Clara Löh , Karin Melnick , Anke Pohl , Freydoon Shahidi , Christopher D. Sogge , Shigeharu Takayama , Hong Wang , Xu-Jia Wang und Yongchang Zhu

Sprache: Englisch

Erstveröffentlichung: 1. Januar 1989

Erscheinungsweise: 6 Hefte pro Jahr

Neuestes Heft anzeigen

Veröffentlicht von

Veröffentlichen auch Sie bei De Gruyter Brill

Manuskript einreichen Informationen für Autor*innen Erkunden Sie dieses Fachgebiet

Über diese Zeitschrift

Objective

Forum Mathematicum (FORUM) is a general mathematics journal, which is devoted to the publication of high-quality research articles in all fields of pure and applied mathematics.

Article formats
Original Articles

> Information on submission process

Ihre Vorteile

Your benefits:

Top journal in the field
Wide range of topics
High quality peer-review
Ahead of print publication

Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

p-adic Rankin–Selberg L-functions in universal deformation families and functional equations

11. September 2025

Zeping Hao, David Loeffler

PDF downloaden

We construct a p -adic Rankin–Selberg L -function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at p ). This gives a function on a four-dimensional base space – strictly larger than the ordinary eigenvariety, which is three-dimensional in this case. We prove our p -adic L -function interpolates all critical values of the Rankin–Selberg L -functions for the classical specialisations of our family, and derive a functional equation for our p -adic L -function by applying a recent deep result of Helm and Moss on universal γ-factors.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Central limit theorem for Hecke eigenvalues

11. September 2025

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

PDF downloaden

In this paper, we obtain the central limit theorem of Hecke eigenvalues in the very general setting of split simple algebraic groups over ℚ, using irreducible characters of compact Lie groups.
Open Access
The limit of a nonlocal p-Laplacian obstacle problem with nonhomogeneous term as p → ∞

29. August 2025

Samer Dweik

PDF downloaden

The aim of this paper is to investigate the asymptotic behavior of the minimizers to the following problems related to the fractional p -Laplacian with nonhomogeneous term h p ⁢ ( x , u ) {{h_{p}(x,u)}} in the presence of an obstacle ψ in a bounded Lipschitz domain Ω ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} , min ⁡ { 1 2 ⁢ ∫ Ω × Ω | u ⁢ ( x ) - u ⁢ ( y ) | p | x - y | α ⁢ p + ∫ Ω h p ⁢ ( x , u ) : u ∈ W s , p ⁢ ( Ω ) , u ≥ ψ ⁢ on ⁢ Ω ¯ , u = g ⁢ on ⁢ ∂ ⁡ Ω } . \min\biggl{\{}\frac{1}{2}\int_{\Omega\times\Omega}\frac{|u(x)-u(y)|^{p}}{|x-y|% ^{\alpha p}}+\int_{\Omega}{{{h_{p}(x,u)}}}:u\in W^{s,p}(\Omega),\,u\geq\psi% \text{ on }\bar{\Omega},\,u=g\text{ on }\partial\Omega\bigg{\}}. In the case when h p ⁢ ( x , u ) = h ⁢ ( x , u ) p p {h_{p}(x,u)=\frac{{h(x,u)}^{p}}{p}} and h ⁢ ( x , u ) ≥ 0 {h(x,u)\geq 0} , we show the convergence of the solutions to certain limit as p → ∞ {p\to\infty} and identify the limit equation. More precisely, we show that the limit problem is closely related to the infinity fractional Laplacian. In the particular case when ∂ s ⁡ h > 0 {\partial_{s}h>0} , we study the Hölder regularity of any solution to the limit problem and we extend the existence result to the case when h is not smooth. In addition, we will study the limit of this problem when the nonhomogeneous term h p ⁢ ( x , u ) {h_{p}(x,u)} is not necessarily positive. To be more precise, we will consider the following two cases: h p ⁢ ( x , u ) = h ⁢ ( x ) ⁢ u {h_{p}(x,u)=h(x)\,u} and h p ⁢ ( x , u ) = h ⁢ ( x ) ⁢ | u | Λ Λ {h_{p}(x,u)=h(x)\,\frac{\,\,|u|^{\Lambda}}{\Lambda}} with Λ := Λ ⁢ ( p ) < p {\Lambda:=\Lambda(p)<p} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

On the abscissae of Weil representation zeta functions for procyclic groups

29. August 2025

Steffen Kionke

PDF downloaden

A famous conjecture of Chowla on the least primes in arithmetic progressions implies that the abscissa of convergence of the Weil representation zeta function for a procyclic group G only depends on the set S of primes dividing the order of G and that it agrees with the abscissa of the Dedekind zeta function of ℤ [ p - 1 ∣ p ∉ S ] {\mathbb{Z}[p^{-1}\mid p\not\in S]} . Here we show that these consequences hold unconditionally for random procyclic groups in a suitable model. As a corollary, every real number 1 ≤ β ≤ 2 {1\leq\beta\leq 2} is the Weil abscissa of some procyclic group.
Open Access
On the Cauchy problem of spherical capillary water waves

29. August 2025

Chengyang Shao

PDF downloaden

The spherical capillary water waves equation describes the motion of an almost spherical water droplet under zero gravity governed by water-air interface tension. Using para-differential calculus on compact Lie groups and homogeneous spaces developed by the author, the system is symmetrized into a quasi-linear dispersive para-differential equation of order 1.5 defined on the 2-sphere. An immediate consequence of this symmetrization is a new proof of local well-posedness of the system under much weaker regularity assumption compared to previous results.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Non-vanishing mod p of theta lifts for (O_2n+1, Mp_4n)

1. August 2025

Xiaoyu Zhang

PDF downloaden

We establish the non-vanishing mod p of global theta lifts from an odd definite orthogonal group O 2 ⁢ n + 1 {\mathrm{O}_{2n+1}} over ℚ {\mathbb{Q}} to a metaplectic group Mp 4 ⁢ n {\mathrm{Mp}_{4n}} over ℚ {\mathbb{Q}} under mild conditions. The problem is closely related to non-vanishing modulo p of toric integrals on O 2 ⁢ n + 1 {\mathrm{O}_{2n+1}} . For this, we exploit the distribution properties of toric orbits of unipotent elements on O 2 ⁢ n + 1 ⁢ ( ℚ ℓ ) {\mathrm{O}_{2n+1}(\mathbb{Q}_{\ell})} using Ratner’s theorems on unipotent flows and we deduce that the toric integral of a p -primitive automorphic form on O 2 ⁢ n + 1 {\mathrm{O}_{2n+1}} is non-zero modulo p for infinitely many characters.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds

1. August 2025

Jean-Claude Cuenin

PDF downloaden

We prove eigenvalue bounds for Schrödinger operator - Δ g + V {-\Delta_{g}+V} on compact manifolds with complex potentials V . The bounds depend only on an L q {L^{q}} -norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank’s [R. L. Frank, Eigenvalue bounds for Schrödinger operators with complex potentials, Bull. Lond. Math. Soc. 43 2011, 4, 745–750] results in the Euclidean case.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Functional inequalities related to Sobolev, Besov and Morrey spaces in the Dunkl setting

1. August 2025

Zhiyong Wang, Pengtao Li, Yu Liu

PDF downloaden

In this paper we investigate the Sobolev inequality in the Dunkl setting using the semigroup theory and a nonlocal calculus for the fractional Dunkl operator. As an application and improvement, we further study some important functional inequalities related to Besov spaces and Morrey spaces.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Global well-posedness of the stochastic electrokinetic flow with the mixed boundary conditions

23. Juli 2025

Zhaoyang Qiu, Huaqiao Wang

PDF downloaden

We investigate the stochastic electrokinetic flow modelled by a stochastic Nernst–Planck–Navier–Stokes system with a blocking boundary condition for ionic species concentrations in a smooth bounded domain 𝒟. In both 2 ⁢ D 2D and 3 ⁢ D 3D cases, we establish the global existence of weak martingale solutions when the capacitance ς > 0 \varsigma>0 , and also establish the existence of a unique maximal strong pathwise solution when the capacitance ς = 0 \varsigma=0 . Moreover, by a probability estimate, we build the blow-up criterion. We finally show that the maximal pathwise solution is global in the 2 ⁢ D 2D case without the restriction of smallness of initial data. In particular, the mixed boundary condition and the random effect bring essential difficulties in constructing approximate solutions and obtaining the a priori estimates which are totally different from the deterministic case. We develop the L 1 L^{1} -energy conservation and the linearization techniques to overcome these difficulties.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Small gaps between almost-twin primes

16. Juli 2025

Bin Chen

PDF downloaden

Let m ∈ N m\in\mathbb{N} be large. We show that there exist infinitely many primes q 1 < ⋯ < q m + 1 q_{1}<\cdots<q_{m+1} such that q m + 1 − q 1 = O ⁢ ( e 7.63 ⁢ m ) q_{m+1}-q_{1}=O(e^{7.63m}) and q j + 2 q_{j}+2 has at most 7.36 ⁢ m log ⁡ 2 + 4 ⁢ log ⁡ m log ⁡ 2 + 21 \frac{7.36m}{\log 2}+\frac{4\log m}{\log 2}+21 prime factors for each 1 ≤ j ≤ m + 1 1\leq j\leq m+1 . This improves the previous result of Li and Pan, replacing m 4 ⁢ e 8 ⁢ m m^{4}e^{8m} by e 7.63 ⁢ m e^{7.63m} and 16 ⁢ m log ⁡ 2 + 5 ⁢ log ⁡ m log ⁡ 2 + 37 \frac{16m}{\log 2}+\frac{5\log m}{\log 2}+37 by 7.36 ⁢ m log ⁡ 2 + 4 ⁢ log ⁡ m log ⁡ 2 + 21 \frac{7.36m}{\log 2}+\frac{4\log m}{\log 2}+21 . The main inputs are the Maynard–Tao sieve, a minorant for the indicator function of the primes constructed by Baker and Irving, for which a stronger equidistribution theorem in arithmetic progressions to smooth moduli is applicable, and Tao’s approach previously used to estimate ∑ x ≤ n < 2 ⁢ x 1 P ⁢ ( n ) ⁢ 1 P ⁢ ( n + 12 ) ⁢ ω n \sum_{x\leq n<2x}\mathbf{1}_{\mathbb{P}}(n)\mathbf{1}_{\mathbb{P}}(n+12)\omega_{n} , where 1 P \mathbf{1}_{\mathbb{P}} stands for the characteristic function of the primes and ω n \omega_{n} are multidimensional sieve weights.
Open Access
Moments of primes in progressions to a large modulus

9. Juli 2025

Sun-Kai Leung

PDF downloaden

Assuming a uniform q -variant of the prime k -tuple conjecture, we compute moments of the number of primes in arithmetic progressions to a large modulus q as the residue classes vary. Consequently, depending on the size of φ ⁢ ( q ) {\varphi(q)} , the prime count follows either a Gaussian or a Poisson distribution. In particular, the least prime in progressions follows an exponential distribution, with some unexpected discrepancies observed for smooth moduli.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

The center of the Hecke algebra of a type

9. Juli 2025

Reda Boumasmoud, Radhika Ganapathy

PDF downloaden

We describe the center of the Hecke algebra of a type attached to a Bernstein block under a certain natural hypothesis. In particular, our hypothesis holds for the types considered by Kim–Yu and Fintzen and thus holds, under a mild tameness hypothesis, for all Bernstein blocks. We use our results to give a description of the Bernstein center of the Hecke algebra ℋ ⁢ ( 𝐆 ⁢ ( F ) , K ) {\mathcal{H}({\bf G}(F),K)} when K belongs to a nice family of compact open subgroups of 𝐆 ⁢ ( F ) {{\bf G}(F)} (which includes the Moy–Prasad filtrations of an Iwahori subgroup) via the theory of types.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Separability properties of extended admissible groups

28. Juni 2025

Hoang Thanh Nguyen

PDF downloaden

Extended admissible groups belong to a particular class of graph of groups which possess a graph of groups decomposition generalizing that of any non-geometric 3-manifold and Croke–Kleiner admissible groups. In this paper, under mild conditions on vertex groups of an extended admissible group G , we show that finitely generated abelian subgroups of G are separable (in particular G is residually finite and has solvable word problem), cohomologically good, and the profinite topology on G is efficient. These results extend those in [E. Hamilton, Abelian subgroup separability of Haken 3-manifolds and closed hyperbolic n -orbifolds, Proc. Lond. Math. Soc. (3) 83 2001, 3, 626–646] and [H. Wilton and P. Zalesskii, Profinite properties of graph manifolds, Geom. Dedicata 147 2010, 29–45] from 3-manifold groups to a wider class of graphs of groups. Finally, we establish that G has property (QT) in the sense of Bestvina–Bromberg–Fujiwara.
Open Access
Log-correlation for shifted Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields

28. Juni 2025

Po-Han Hsu, Peng-Jie Wong

PDF downloaden

Adapting a method of Radziwiłł and Soundararajan, we prove a generalisation of Bourgade’s central limit theorem (on shifted Riemann zeta functions) for Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields. As an application, we obtain logarithmic correlation results for shifted Dirichlet 𝐿-functions and shifted Dedekind zeta functions. These are inspired by two assumptions regarding the joint value distribution of two given shifted Riemann zeta functions, considered by Harper in le séminaire Nicolas Bourbaki.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Unipotent mixing for general moduli

25. Juni 2025

Edgar Assing

PDF downloaden

In this note we prove a joint equidistribution result for discrete low lying horocycles. This generalizes previous work of Blomer and Michel, where it was crucially assumed that the number of discrete points is prime.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Subconvex bound for GL(3) × GL(2) L-functions: GL(3)-spectral aspect

29. Mai 2025

Sumit Kumar, Kummari Mallesham, Saurabh Kumar Singh

PDF downloaden

Let ϕ be a Hecke–Maass cusp form for SL ⁢ ( 3 , ℤ ) {\mathrm{\mathrm{SL}(3,\mathbb{Z})}} with Langlands parameters ( 𝐭 i ) i = 1 3 {({\bf t}_{i})_{i=1}^{3}} and let f be a holomorphic or Hecke–Maass cusp form for SL ⁢ ( 2 , ℤ ) {\mathrm{\mathrm{SL}(2,\mathbb{Z})}} . In this article we prove the following subconvex bound: L ⁢ ( ϕ × f , 1 2 ) ≪ f , ϵ T 3 2 - δ ξ + ϵ , δ ξ = min ⁡ { ξ 4 , 1 4 ⁢ ( 1 - 2 ⁢ ξ ) } , L(\phi\times f,\tfrac{1}{2})\ll_{f,\epsilon}T^{\frac{3}{2}-\delta_{\xi}+% \epsilon},\quad\delta_{\xi}=\min\{\tfrac{\xi}{4},\tfrac{1}{4}(1-2\xi)\}, for the central value L ⁢ ( ϕ × f , 1 2 ) {L(\phi\times f,\frac{1}{2})} in the GL ⁢ ( 3 ) {\mathrm{GL}(3)} -spectral aspect, where ( 𝐭 i ) i = 1 3 {({\bf t}_{i})_{i=1}^{3}} satisfies | 𝐭 3 - 𝐭 2 | ≍ T 1 - ξ , 𝐭 i ≍ T , i = 1 , 2 , 3 , |{\bf t}_{3}-{\bf t}_{2}|\asymp T^{1-\xi},\quad{\bf t}_{i}\asymp T,\quad i=1,2% ,3, with ξ a real number such that 0 < ξ < 1 2 {0<\xi<\frac{1}{2}} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Continuity properties of multi-parameter pseudodifferential operators

29. Mai 2025

Wei Ding, Xiaodong Ding, Yueping Zhu

PDF downloaden

It is well known that an pseudodifferential operator T σ {T_{\sigma}} with σ ∈ S ρ , δ m ⁢ ( ℝ n ) {\sigma\in S^{m}_{\rho,\delta}(\mathbb{R}^{n})} is bounded on L 2 ⁢ ( ℝ n ) {L^{2}(\mathbb{R}^{n})} if m ≤ 0 , m + n 2 ⁢ ( δ - ρ ) < 0 {m\leq 0,m+\frac{n}{2}(\delta-\rho)<0} which was established by Hörmander. In this paper, we generalize this result to multi-parameter pseudodifferential operators. Using the atomic decomposition theory, we obtain the boundedness from h p ⁢ ( ℝ n 1 × ℝ n 2 ) {h^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} to L p ⁢ ( ℝ n 1 + n 2 ) {L^{p}(\mathbb{R}^{n_{1}+n_{2}})} of bi-parameter pseudodifferential operators for 0 < p ≤ 1 {0<p\leq 1} . Calderón–Zygmund decomposition and interpolation theory on h p ⁢ ( ℝ n 1 × ℝ n 2 ) {h^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} are also established.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Shifting the ordinates of zeros of the Riemann zeta function

29. Mai 2025

William Banks

PDF downloaden

Let y ≠ 0 y\neq 0 and C > 0 C>0 . Under the Riemann Hypothesis, there is a number T * > 0 T_{*}>0 (depending on y and C ) such that for every T ⩾ T * T\geqslant T_{*} , both ζ ⁢ ( 1 2 + i ⁢ γ ) = 0 and ζ ⁢ ( 1 2 + i ⁢ ( γ + y ) ) ≠ 0 \zeta(\frac{1}{2}+i\gamma)=0\quad\mbox{and}\quad\zeta(\frac{1}{2}+i(\gamma+y))\neq 0 hold for at least one γ in the interval [ T , T ⁢ ( 1 + ε ) ] [T,T(1+\varepsilon)] , where ε := T - C log ⁡ log ⁡ T \varepsilon:=T^{-\frac{C}{\log\log T}} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Diagonals of solutions of the Yang–Baxter equation

29. Mai 2025

Přemysl Jedlicka, Agata Pilitowska

PDF downloaden

We study the diagonal mappings in non-involutive set-theoretic solutions of the Yang–Baxter equation. We show that, for non-degenerate solutions, they are commuting bijections. This gives the positive answer to the question: “Is every non-degenerate solution bijective?” of Cedó, Jespers and Verwimp. Additionally, we show that, for a subclass of solutions called k - permutational , only one-sided non-degeneracy suffices to prove that one of the diagonal mappings is invertible. We also present an equational characterization of multipermutation solutions and extend results of Rump, Gateva–Ivanova and Castelli, Mazzotta, Stefanelli about decomposability to non-involutive infinite case. In particular, we show that each, not necessarily involutive, square-free multipermutation solution of finite level and arbitrary cardinality, is always decomposable.
Open Access
The sum of a prime power and an almost prime

29. Mai 2025

Daniel R. Johnston, Simon N. Thomas

PDF downloaden

For any fixed k ≥ 2 {k\geq 2} , we prove that every sufficiently large integer can be expressed as the sum of a k th power of a prime and a number with at most M ⁢ ( k ) = 6 ⁢ k {M(k)=6k} prime factors. For sufficiently large k we also show that one can take M ⁢ ( k ) = ( 2 + ε ) ⁢ k {M(k)=(2+\varepsilon)k} for any ε > 0 {\varepsilon>0} , or M ⁢ ( k ) = ( 1 + ε ) ⁢ k {M(k)=(1+\varepsilon)k} under the assumption of the Elliott–Halberstam conjecture. Moreover, we give a variant of this result which accounts for congruence conditions and strengthens a classical theorem of Erdős and Rao. The main tools we employ are the weighted sieve method of Diamond, Halberstam and Richert, bounds on the number of representations of an integer as the sum of two k th powers, and results on k th power residues. We also use some simple computations and arguments to conjecture an optimal value of M ⁢ ( k ) {M(k)} , as well as a related variant of Hardy and Littlewood’s Conjecture H.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Sharp constants for fractional Hardy–Littlewood maximal operators on finite graphs

29. Mai 2025

Chenghao Xiang, Fayou Zhao

PDF downloaden

For 0 ≤ α < 1 {0\leq\alpha<1} , let M α , G {M_{\alpha,G}} be the fractional Hardy–Littlewood maximal operator on the finite graph G . If 0 < p ≤ q ≤ 1 {0<p\leq q\leq 1} , we obtain lower bounds and upper bounds for C G , q {C_{G,q}} such that the inequality ∥ M α , G ⁢ f ∥ q ≤ C G , q ⁢ ∥ f ∥ p {\|M_{\alpha,G}f\|_{q}\leq C_{G,q}\|f\|_{p}} holds and the complete graphs K n {K_{n}} and star graphs S n {S_{n}} are two extreme graphs that reach the lower bound and upper bound respectively. If 1 < p < + ∞ {1<p<+\infty} , we prove the existence of the extremizers for ∥ M α , K n ∥ ℓ p → ℓ p {\|M_{\alpha,K_{n}}\|_{\ell^{p}\to\ell^{p}}} and ∥ M α , S n ∥ ℓ p → ℓ p {\|M_{\alpha,S_{n}}\|_{\ell^{p}\to\ell^{p}}} . If p = 2 {p=2} , we calculate the value of the norm ∥ M α , G ∥ ℓ 2 → ℓ 2 {\|M_{\alpha,G}\|_{\ell^{2}\to\ell^{2}}} when (i) G = K n {G=K_{n}} , n ≥ 2 {n\geq 2} and 0 ≤ α < 1 {0\leq\alpha<1} ; (ii) G = S n {G=S_{n}} , n ≥ 4 {n\geq 4} and 0 ≤ α ≤ 1 2 - 1 2 ⁢ log n 2 ⁡ 2 {0\leq\alpha\leq\frac{1}{2}-\frac{1}{2}\log_{\frac{n}{2}}2} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

A density version of Hua’s theorem

29. April 2025

Maoru Tan

PDF downloaden

Let ℙ {\mathbb{P}} be the set of primes. Given five sets P i {P_{i}} , i = 1 , 2 , 3 , 4 , 5 {i=1,2,3,4,5} , in ℙ {\mathbb{P}} with relative lower density d ¯ ℙ ⁢ ( P i ) = ε i {\underline{d}_{\mathbb{P}}(P_{i})=\varepsilon_{i}} , we prove that given the condition that ∑ i = 1 5 ε i 2 > 4 {\sum_{i=1}^{5}\varepsilon_{i}^{2}>4} , every sufficiently large number n ≡ 5 ⁢ ( mod ⁢ 24 ) {n\equiv 5\mskip 4.0mu (\mathrm{mod}\mskip 6.0mu 24)} can be written as n = ∑ i = 1 5 p i 2 {n=\sum_{i=1}^{5}p_{i}^{2}} with p i ∈ P i {p_{i}\in P_{i}} , i = 1 , 2 , 3 , 4 , 5 {i=1,2,3,4,5} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

The L ²-unique continuation property on manifolds with bounded geometry and the deformation operator

29. April 2025

Nadine Große, Mirela Kohr, Victor Nistor

PDF downloaden

By definition, a differential operator T on a connected manifold satisfies the L 2 {L^{2}} -unique continuation property if every L 2 {L^{2}} -solution of T that vanishes on an open subset vanishes identically. We study the L 2 {L^{2}} -unique continuation property of an operator T acting on a manifold with bounded geometry. In particular, we establish some connections between this property and the regularity properties of T . As an application, we prove that the deformation operator on a manifold with bounded geometry satisfies regularity and L 2 {L^{2}} -unique continuation properties. As another application, we prove that suitable elliptic operators are invertible (Hadamard well-posedness). Our results apply, in particular, to compact manifolds, as all such manifolds have bounded geometry.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Space-time estimate for the perturbed linear elastic wave equations exterior to a ball with radial data and its application

29. April 2025

Wei Xu, Ning-An Lai

PDF downloaden

In this paper we are devoted to establishing a kind of weighted space-time estimate for the perturbed linear elastic wave equations in the exterior domain outside a ball in ℝ 3 {{\mathbb{R}}^{3}} , assuming the initial data are radial symmetric. This solves an interesting open problem posed in [J. Metcalfe and C. D. Sogge, Global existence of null-form wave equations in exterior domains, Math. Z. 256 2007, 3, 521–549] in the radial symmetric case. As an application, we prove the almost global existence for the nonlinear elastic wave equations in the domain exterior to a ball with inhomogeneous boundary condition and radial symmetric initial data.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

A characterization of unitarity of some highest weight Harish-Chandra modules

29. April 2025

Zhanqiang Bai, Markus Hunziker

PDF downloaden

Let L ⁢ ( λ ) {L(\lambda)} be a highest weight Harish-Chandra module with highest weight λ. When the associated variety of L ⁢ ( λ ) {L(\lambda)} is not maximal, that is, not equal to the nilradical of the corresponding parabolic subalgebra, we prove that the unitarity of L ⁢ ( λ ) {L(\lambda)} can be determined by a simple condition on the value of z = ( λ + ρ , β ∨ ) {z=(\lambda+\rho,\beta^{\vee})} , where ρ is half the sum of positive roots and β is the highest root. In the proof, certain distinguished antichains of positive noncompact roots play a key role. By using these antichains, we are also able to provide a uniform formula for the Gelfand–Kirillov dimension of all highest weight Harish-Chandra modules, generalizing our previous result for the case of unitary highest weight Harish-Chandra modules.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

The 3D incompressible anisotropic magnetic Bénard system with fractional partial dissipation

9. April 2025

Yujun Liu

PDF downloaden

In this paper, we consider the global strong solution to the 3D incompressible anisotropic magnetic Bénard system with fractional partial dissipation. It is well known that the global regularity or finite time singularity of the classical solution for the 3D Navier–Stokes and magnetohydrodynamic (MHD) equations remains an outstanding open problem. The same problem for the 3D incompressible anisotropic magnetic Bénard system with fractional partial dissipation is also difficult. For the initial data ( u 0 , b 0 , θ 0 ) ∈ H 1 ⁢ ( R 3 ) (\mathbf{u}_{0},\mathbf{b}_{0},\theta_{0})\in H^{1}(\mathbb{\mathbb{R}}^{3}) , we establish the global-in-time existence and uniqueness strong solutions to the 3D incompressible anisotropic magnetic Bénard system with fractional partial velocity dissipation and magnetic diffusion and thermal diffusion.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Spherical Shalika models on PGU_2,2 and the theta correspondence for (PGSp₄, PGU_2,2)

28. März 2025

Antonio Cauchi, Armando Gutierrez Terradillos

PDF downloaden

We study Shalika models for generic unramified representations of PGU 2 , 2 {{\rm PGU}_{2,2}} over non-archimedean local fields of characteristic zero. We show that they are unique up to constant by means of the theta correspondence for ( PGSp 4 , PGU 2 , 2 ) {(\mathrm{P}{{\rm GSp}}_{4},{\rm PGU}_{2,2})} . We then prove a Casselman–Shalika formula which relates the values of spherical Shalika functionals on PGU 2 , 2 {{\rm PGU}_{2,2}} to the values of finite-dimensional complex representations of the dual group of PGSp 4 {\mathrm{P}{{\rm GSp}}_{4}} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Key subgroups in topological groups

28. März 2025

Michael Megrelishvili, Menachem Shlossberg

PDF downloaden

We introduce two minimality properties of subgroups in topological groups. A subgroup H is a key subgroup ( co-key subgroup ) of a topological group G if there is no strictly coarser Hausdorff group topology on G which induces on H (resp., on the coset space G / H {G/H} ) the original topology. Every co-minimal subgroup is a key subgroup while the converse is not true. Every locally compact co-compact subgroup is a key subgroup (but not always co-minimal). Any relatively minimal subgroup is a co-key subgroup (but not vice versa). Extending some results from [M. Megrelishvili, Group representations and construction of minimal topological groups, Topology Appl. 62 1995, 1, 1–19] and [D. Dikranjan and M. Megrelishvili, Relative minimality and co-minimality of subgroups in topological groups, Topology Appl. 157 2010, 1, 62–76] concerning the generalized Heisenberg groups, we prove that the center (“corner” subgroup) of the upper unitriangular group UT ⁢ ( n , K ) {\mathrm{UT(n,K)}} , defined over a commutative topological unital ring K , is a key subgroup. Every “non-corner” 1-parameter subgroup H of UT ⁢ ( n , K ) {\mathrm{UT(n,K)}} is a co-key subgroup. We study injectivity property of the restriction map r H : 𝒯 ↓ ⁢ ( G ) → 𝒯 ↓ ⁢ ( H ) {r_{H}:\mathcal{T}_{\downarrow}(G)\to\mathcal{T}_{\downarrow}(H)} , σ ↦ σ | H {\sigma\mapsto\sigma|_{H}} and show that it is an isomorphism of sup-semilattices for every central co-minimal subgroup H , where 𝒯 ↓ ⁢ ( G ) {\mathcal{T}_{\downarrow}(G)} is the semilattice of coarser Hausdorff group topologies on G .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Eisenstein series modulo p ²

28. März 2025

Scott Ahlgren, Michael Hanson, Martin Raum, Olav K. Richter

PDF downloaden

We study congruences for Eisenstein series on SL 2 ⁢ ( ℤ ) {{\rm SL}_{2}(\mathbb{Z})} modulo p 2 {p^{2}} , where p ≥ 5 {p\geq 5} is prime. It is classically known that all Eisenstein series of weight at least 4 are determined modulo p 2 {p^{2}} by those of weight at most p 2 - p + 2 {p^{2}-p+2} . We prove that up to powers of E p - 1 {E_{p-1}} , each such Eisenstein series is in fact determined modulo p 2 {p^{2}} by a modular form of weight at most 2 ⁢ p - 4 {2p-4} . We also determine E 2 {E_{2}} modulo p 2 {p^{2}} in terms of a modular form of weight p + 1 {p+1} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Harish-Chandra theorem for two-parameter quantum groups

28. März 2025

Naihong Hu, Hengyi Wang

PDF downloaden

This paper is devoted to investigating the center of two-parameter quantum groups U r , s ⁢ ( 𝔤 ) {U_{r,s}(\mathfrak{g})} via establishing the Harish-Chandra homomorphism. Based on the Rosso form and the representation theory of weight modules, we prove that when the rank 𝔤 {\mathfrak{g}} is even, the Harish-Chandra homomorphism is an isomorphism, and in particular, the center of the quantum group U ˘ r , s ⁢ ( 𝔤 ) {\breve{U}_{r,s}(\mathfrak{g})} of the weight lattice type is a polynomial algebra 𝕂 ⁢ [ z ϖ 1 , … , z ϖ n ] {\mathbb{K}[z_{\varpi_{1}},\dots,z_{\varpi_{n}}]} , where canonical central elements z λ {z_{\lambda}} ( λ ∈ Λ + {\lambda\in\Lambda^{+}} ) are turned out to be uniformly expressed. For the rank 𝔤 {\mathfrak{g}} to be odd, we figure out a new invertible extra central generator z * {z_{*}} , which does not survive in U q ⁢ ( 𝔤 ) {U_{q}(\mathfrak{g})} , then the center of U ˘ r , s ⁢ ( 𝔤 ) {\breve{U}_{r,s}(\mathfrak{g})} contains 𝕂 ⁢ [ z ϖ 1 , … , z ϖ n ] ⊗ 𝕂 𝕂 ⁢ [ z * 1 ℓ , z * - 1 ℓ ] {\mathbb{K}[z_{\varpi_{1}},\dots,z_{\varpi_{n}}]\otimes_{\mathbb{K}}\mathbb{K}% [z_{*}^{{\frac{1}{\ell}}},z_{*}^{{-\frac{1}{\ell}}}]} , where ℓ = 2 {\ell=2} , except ℓ = 4 {\ell=4} for D 2 ⁢ k + 1 {D_{2k+1}} .
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

On Stein spaces with finite homotopy rank-sum

28. März 2025

Indranil Biswas, Buddhadev Hajra

PDF downloaden

A topological space (not necessarily simply connected) is said to have finite homotopy rank-sum if the sum of the ranks of all higher homotopy groups (from the second homotopy group onward) is finite. In this article, we consider Stein spaces of arbitrary dimension satisfying the above rational homotopy theoretic property, although most of this article focuses on Stein surfaces only. We characterize all Stein surfaces satisfying the finite homotopy rank-sum property. In particular, if such a Stein surface is affine and every element of its fundamental group is finite, it is either simply connected or has a fundamental group of order 2. A detailed classification of the smooth complex affine surfaces of the non-general type satisfying the finite homotopy rank-sum property is obtained. It turns out that these affine surfaces are Eilenberg–MacLane spaces whenever the fundamental group is infinite.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Graphs represented by Ext

28. März 2025

Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah

PDF downloaden

This paper opens and discusses the question originally due to Daniel Herden, who asked for which graph ( μ , R ) {(\mu,R)} we can find a family { 𝔾 α : α < μ } {\{\mathbb{G}_{\alpha}:\alpha<\mu\}} of abelian groups such that for each α , β ∈ μ {\alpha,\beta\in\mu} , Ext ⁢ ( 𝔾 α , 𝔾 β ) = 0 {{\rm Ext}(\mathbb{G}_{\alpha},\mathbb{G}_{\beta})=0} iff ( α , β ) ∈ R {(\alpha,\beta)\in R} . In this regard, we present four results. First, we give a connection to Quillen’s small object argument which helps Ext {{\rm Ext}} vanishes and use it to present a useful criteria to the question. Suppose λ = λ ℵ 0 {\lambda=\lambda^{\aleph_{0}}} and μ = 2 λ {\mu=2^{\lambda}} . We apply Jensen’s diamond principle along with the criteria to present λ-free abelian groups representing bipartite graphs. Third, we use a version of the black box to construct in ZFC, a family of ℵ 1 {\aleph_{1}} -free abelian groups representing bipartite graphs. Finally, applying forcing techniques, we present a consistent positive answer for general graphs.
Open Access
On integral aspects of Asai periods and Euler systems for Res_E/ℚGL₂

11. März 2025

Alexandros Groutides

PDF downloaden

Let E / ℚ {E/\mathbb{Q}} be a totally real quadratic field. Using unramified harmonic analysis in Hecke modules, we study the ℓ {\ell} -adic integral behavior of the (unramified part of the) Asai period attached to a Hilbert modular form for E , when evaluated on arbitrary integral test data in the sense of [D. Loeffler, On some zeta-integrals for unramified representations of gsp(4), preprint 2021, https://arxiv.org/abs/2106.16076]. Using the same representation-theoretic framework, we also prove the conjectured integral behavior of local factors appearing in tame norm relations, between any collection of integral motivic Asai–Flach classes in the recipe of [D. Loeffler, C. Skinner and S. L. Zerbes, An Euler system for GU ⁢ ( 2 , 1 ) \rm GU(2,1) , Math. Ann. 382 2022, 3–4, 1091–1141]. Finally, specializing to one such specific integral collection, we obtain the most general version of the Asai–Flach Euler system tame norm relations, extending a result of [G. Grossi, On norm relations for Asai–Flach classes, Int. J. Number Theory 16 2020, 10, 2311–2377].
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

Spherical characters in families: The unitary Gan–Gross–Prasad case

1. März 2025

Li Cai, Yangyu Fan

PDF downloaden

We consider the variation of spherical characters in families. We formulate conjectures for the rationality and meromorphic property of spherical characters. As an example, we establish these conjectures in the unitary Gan–Gross–Prasad case.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

L ²-exponential ergodicity of stochastic Hamiltonian systems with α-stable Lévy noises

25. Februar 2025

Jianhai Bao, Jian Wang

PDF downloaden

Based on the hypocoercivity approach due to Villani (2009), Dolbeault, Mouhot and Schmeiser (2015) established a new and simple framework to investigate directly the L 2 {L^{2}} -exponential convergence to the equilibrium for the solution to the kinetic Fokker–Planck equation. Nowadays, the general framework advanced by Dolbeault, Mouhot and Schmeiser (2015) is named as the DMS framework for hypocoercivity. Subsequently, Grothaus and Stilgenbauer (2014) built a dual version of the DMS framework in the kinetic Fokker–Planck setting. No matter what the abstract DMS framework by Dolbeault, Mouhot and Schmeiser (2015) or the dual counterpart by Grothaus and Stilgenbauer (2014), the densely defined linear operator involved is assumed to be decomposed into two parts, where one part is symmetric and the other part is anti-symmetric. Thus, the existing DMS framework is not applicable to investigate the L 2 {L^{2}} -exponential ergodicity for stochastic Hamiltonian systems with α-stable Lévy noises, where one part of the associated infinitesimal generators is anti-symmetric whereas the other one is not symmetric at all. In this paper, we shall develop a dual version of the DMS framework in the fractional kinetic Fokker–Planck setup, where one part of the densely defined linear operator under consideration need not to be symmetric. As a direct application, we explore the L 2 {L^{2}} -exponential ergodicity of stochastic Hamiltonian systems with α-stable Lévy noises. The proof is also based on Poincaré inequalities for non-local stable-like Dirichlet forms and the potential theory for fractional Riesz potentials.
Erfordert eine Authentifizierung Nicht lizenziert
Lizenziert

A bridge between convexity and quasiconvexity

21. Februar 2025

Pablo Blanc, Mikko Parviainen, Julio D. Rossi

PDF downloaden

We introduce a notion of convexity with respect to a one-dimensional operator and with this notion find a one-parameter family of different convexities that interpolates between classical convexity and quasiconvexity. We show that, for this interpolation family, the convex envelope of a continuous boundary datum in a strictly convex domain is continuous up to the boundary and is characterized as being the unique viscosity solution to the Dirichlet problem in the domain for a certain fully nonlinear partial differential equation that involves the associated operator. In addition we prove that the convex envelopes of a boundary datum constitute a one-parameter curve of functions that goes from the quasiconvex envelope to the convex envelope being continuous with respect to uniform convergence. Finally, we also show some regularity results for the convex envelopes proving that there is an analogous to a supporting hyperplane at every point and that convex envelopes are C 1 {C^{1}} if the boundary data satisfies in particular NV-condition we introduce.
Öffentlich zugänglich
Notice of retraction

18. April 2014

PDF downloaden

Abstract. Retraction of http://dx.doi.org/10.1515/forum-2013-0111.
Öffentlich zugänglich
QE-transitive abelian groups

10. Januar 2014

Manfred Dugas

PDF downloaden

Abstract. This article has been retracted due to honest error by the author. For further information, please see http://dx.doi.org/10.1515/forum-2014-0063. Let G be a torsion-free abelian group and n be a (finite) cardinal. The group G is called n -QE-transitive if for any pure subgroups X,Y${X,Y}$ of rank n of G , there exists some endomorphism ϕ of G such that ϕ(X)⊆Y${\varphi (X)\subseteq Y}$ and Y/ϕ(X)${Y/\varphi (X)}$ is a torsion abelian group. We investigate these groups and obtain results similar to the ones for E-transitive groups.

to be implemented...

Heft 0

Heft 37

Heft 36

Heft 35

Heft 34

Heft 33

Heft 32

Heft 31

Heft 30

Heft 29

Heft 28

Heft 27

Heft 26

Heft 25

Heft 24

Heft 23

Heft 22

Heft 21

Heft 20

Heft 19

Heft 18

Heft 17

Heft 16

Heft 15

Heft 14

Heft 13

Heft 12

Heft 11

Heft 10

Heft 9

Heft 8

Heft 7

Heft 6

Heft 5

Heft 4

Heft 3

Heft 2

Heft 1

Journal Impact Factor	0.9	2024, Journal Citation Reports (Clarivate, 2025)
5-year Journal Impact Factor	0.9	2024, Journal Citation Reports (Clarivate, 2025)
Journal Citation Indicator	0.66	2024, Journal Citation Reports (Clarivate, 2025)
CiteScore	1.7	2024, Scopus (Elsevier B.V., 2025)
SCImago Journal Rank	0.868	2024, SJR (Scimago Lab, 2025; Data Source: Scopus)
Source Normalized Impact per Paper	1.128	2024, CWTS Journal Indicators (CWTS B.V., 2025; Data Source: Scopus)
Mathematical Citation Quotient	0.86

Weitere Informationen über Zeitschriftenmetriken

Submission
You can easily submit your manuscript online. Simply go to...
http://mc.manuscriptcentral.com/form
...and you will be guided through the whole peer-reviewing and publishing process.

Your benefits of publishing with us

Rapid online publication ahead-of-print with short turnaround times
High quality manuscript processing through ScholarOne Manuscripts®
Optional open access publication
Accepted papers will be published online first as DOI-citable, forward-linked articles for quickest possible visibility for the scientific community
Every article easily discoverable because of SEO and comprehensive abstracting and indexing services
Secure archiving by De Gruyter and the independent archiving service Portico
Professional sales and marketing activities .

Submission process

Submission of your paper via our submission management tool
Peer review process (you will be guided through every step)
Decision on your paper
If accepted: you have the option to publish it open access
Publication online and in print

Please note

Manuscripts must be written in clear and concise English
Before submitting your article please have a look at our Ethical Guidelines and our Copyright Transfer Agreement
Once your article is accepted you have the option to publish it open access
Our Repository Policy allows you to distribute 30 PDF copies of your published article to colleagues (the PDF has to include the information that it is an author's copy). Please also feel free to distribute the link to the online abstract.
If you have any general questions please visit our FAQ page for authors

We look forward to receiving your manuscript!

Hybrid Open Access

Please note that authors from institutions with which we have a transformative agreement can publish open access without paying an article processing charge (APC). More information on the eligible institutions and articles can be found under the "Funding and Support" tab here.

Editor-in-Chief

Guozhen Lu
Department of Mathematics
University of Connecticut
guozhen.lu@uconn.edu
Primary research areas: Harmonic analysis, partial differential equations and geometric analysis

Associate Editors

Thomas Alazard
CNRS and École Normale Supérieure Paris-Saclay
thomas.alazard@ens-paris-saclay.fr
Primary research areas : partial differential equations,microlocal analysis, mathematical problems in fluid dynamics

Jan H. Bruinier
Department of Mathematics
Technische Universität Darmstadt
bruinier@mathematik.tu-darmstadt.de
Primary research areas: Number theory, automorphic forms, algebraic geometry.

Manfred Droste
Institut für Informatik
Universität Leipzig
droste@informatik.uni-leipzig.de
Primary research areas: Group theory, logic, ordered structures, automata theory.

Maria Del Mar Gonzalez
Departamento de Matemáticas
Universidad Autónoma de Madrid
mariamar.gonzalezn@uam.es
Primary research areas: Conformal geometry,　Non-local PDEs and　Fully non-linear equations

Philipp Habegger
Universität Basel
Departement Mathematik und Informatik
Basel, Schweiz
philipp.habegger@unibas.ch
Primary research areas: Number Theory, Diophantine Geometry

Matthias Hieber
Department of Mathematics
TU Darmstadt, Germany
hieber@mathematik.tu-darmstadt.de
Primary research areas: partial differential equations, fluid dynamics

Clara Löh
Faculty of Mathematics
University of Regensburg
clara.loeh@mathematik.uni-regensburg.de
Primary research areas: Geometric Topology, Geometric Group Theory, Measured Group Theory

Karin Melnick
Department of Mathematics
University of Luxembourg
karin.melnick@uni.lu
Primary research areas: differential geometry, transformation groups

Anke Pohl
Institute for Dynamical Systems
Department 3 - Mathematics
University of Bremen
apohl@uni-bremen.de
Primary research areas: Ergodic theory and dynamical systems, harmonic analysis and spectral theory, symmetric spaces

Freydoon Shahidi
Department of Mathematics
Purdue University
shahidi@math.purdue.edu
Primary research areas: Automorphic forms, group representations, number theory and arithmetic geometry.

Christopher D. Sogge
Department of Mathematics
Johns Hopkins University
sogge@jhu.edu
Primary research areas: Fourier analysis, partial differential equations.

Shigeharu Takayama
Department of Mathematics
University of Tokyo
taka@ms.u-tokyo.ac.jp
Primary research areas: complex geometry, Kähler geometry and algebraic geometry

Hong Wang
Courant Institute of Mathematical Sciences
New York University
hw3639@nyu.edu
Primary research areas: Fourier Analysis and Geometric Measure Theory

Xu-Jia Wang
Institute for Theoretical Sciences
Westlake University
Wangxujia@westlake.edu.cn
Primary research areas: Geometric analysis and partial differential equations

Yongchang Zhu
Department of Mathematics
Hong Kong University of Science and Technology
mazhu@ust.hk
Primary research areas: representation theory, mathematical physics

Editorial Office at De Gruyter

Masha Dorogova
Journal Coordinator Forum Mathematicum
masha.dorogova@degruyter.com

Forum Mathematicum ist in den folgenden Services indiziert:

Baidu Scholar
Cabells Journalytics
CNKI Scholar (China National Knowledge Infrastructure)
CNPIEC - cnpLINKer
Dimensions
EBSCO (relevant databases)
EBSCO Discovery Service
Genamics JournalSeek
Google Scholar
Japan Science and Technology Agency (JST)
J-Gate
Journal Citation Reports/Science Edition
JournalGuide
Mathematical Reviews (MathSciNet)
Naver Academic
Naviga (Softweco)
Primo Central (ExLibris)
ProQuest (relevant databases)
Publons
QOAM (Quality Open Access Market)
ReadCube
ScienceON (Korea Institute of Science and Technology Information)
Scilit
SCImago (SJR)
SCOPUS
Semantic Scholar
Sherpa/RoMEO
Summon (ProQuest)
TDNet
Ulrich's Periodicals Directory/ulrichsweb
WanFang Data
Web of Science - Current Contents/Physical, Chemical and Earth Sciences
Web of Science - Science Citation Index
Web of Science - Science Citation Index Expanded
WorldCat (OCLC)
X-MOL
Yewno Discover
zbMATH Open

Mathematik Mathematik, Allgemeines

Zeitschriften Informationen

Weitere Informationen

eISSN:

1435-5337

ISSN:

0933-7741

Sprache:

Englisch

Verlag:

De Gruyter

Weitere Informationen

Erstveröffentlichung:

1. Januar 1989

Erscheinungsweise:

6 Hefte pro Jahr

eISSN: 1435-5337

ISSN: 0933-7741

Zielgruppe(n) für diese Zeitschrift

researchers in the field of mathematics

Sicherheits- und Produktressourcen

Herstellerinformationen:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Forum Mathematicum

Über diese Zeitschrift

Ihre Vorteile

Zusatzmaterial

Fachgebiete

Forum Mathematicum

Übersicht

Über diese Zeitschrift

Ihre Vorteile

Ahead-of-Publication / Just-Accepted

Ausgaben

Metriken

Einreichen

Editorial

Abstracting und Indexing

Zusatzmaterial

Zusatzmaterial

Fachgebiete

Fachgebiete

Externe Links

Bibliographische Daten