Upper bounds of some special zeros for the Rankin-Selberg L-function
-
Kajtaz H. Bllaca
Abstract
In this paper, we prove some conditional results about the order of zero at central point s = 1/2 of the Rankin-Selberg L-function L(s, πf × π͠′f). Then, we give an upper bound for the height of the first zero with positive imaginary part of L(s, πf × π͠′f). We apply our results to automorphic L-functions.
(Communicated by Filippo Nuccio)
References
[1] Avdispahić, M.—Smajlović, A: Explicit formula for a fundamental class of functions, Bull. Belg. Math. Soc. Simon Stevin 12 (2005), 569–587.10.36045/bbms/1133793345Search in Google Scholar
[2] Cogdell, J.W.: L-functions and converse theorems for GLn, Park City Lect. Notes, available at http://www.math.ohio-state.edu/~cogdell.Search in Google Scholar
[3] Gelbart, S.—Shahidi, F.: Boundedness of automorphic L-functions in vertical strips, J. Am. Math. Soc. 14, (2001), 79–107.10.1090/S0894-0347-00-00351-9Search in Google Scholar
[4] Jacquet, H.—Shalika, J. A.: On Euler products and the classification of automorphic representations, I. Am. J. Math. 103 (1981), 499–558.10.2307/2374103Search in Google Scholar
[5] Jacquet, H.—Shalika, J. A.: On Euler products and the classification of automorphic representations II, Am. J. Math. 103 (1981), 777–815.10.2307/2374050Search in Google Scholar
[6] Jorgenson, J.—Lang, S.: Explicit formulas for regularized series and products, Springer Lecture Notes in Math. 1593, Springer-Verlag, Berlin-Heidelberg, 1994.10.1007/BFb0074039Search in Google Scholar
[7] Mestre, J.-F.: Formules explicites et minorations de conducteurs de variétés algébriques, Compositio Math. 58(2) (1986), 209–232.Search in Google Scholar
[8] Moeglin, C.—Waldspurger, J.-L.: Le spectre residuel deGL(n), Ann. Sci. école Norm. Sup. 22 (1989), 605–674.10.24033/asens.1595Search in Google Scholar
[9] Odžak, A.—Smajlović, L.: On Li’s coefficients for the Rankin-SelbergL-function, Ramanujan J. 21 (2010), 303–334.10.1007/s11139-009-9175-zSearch in Google Scholar
[10] Odžak, A.—Smajlović, L.: On the generalized Euler-Stieltjes constants for the Rankin-SelbergL-function, Int. J. Number Theory 13(6) (2017), 1363–1379.10.1142/S1793042117500762Search in Google Scholar
[11] Omar, S.: Majoration du premier zéro de la fonction zêta de Dedekind, Acta Arith. XCV(1) (2000), 61–65.10.4064/aa-95-1-61-65Search in Google Scholar
[12] Shahidi, F.: On certain L-functions, Am. J. Math. 103 (1981), 297–355.10.2307/2374219Search in Google Scholar
[13] Shahidi, F.: Fourier transforms of intertwinting operators and Plancherel measures forGL(n), Am. J. Math. 106 (1984), 67–111.10.2307/2374430Search in Google Scholar
[14] Shahidi, F.: Local coefficients as Artin factors for real groups, Duke Math. J. 52 (1985), 973–1007.10.1215/S0012-7094-85-05252-4Search in Google Scholar
[15] Shahidi, F.: A proof of Langland’s conjecture on Plancherel measures, complementary series for p-adic groups, Ann. Math. 132 (1990), 273–330.10.2307/1971524Search in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
Articles in the same Issue
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
