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L∞ norms of holomorphic modular forms in the case of compact quotient
-
Soumya Das
und
Jyoti Sengupta
Veröffentlicht/Copyright:
5. Juli 2015
Abstract
We prove a sub-convex estimate for the sup-norm of L2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over ℚ. More precisely we show that when the L2 norm of an eigenfunction f is one,
for any
Funding source: DST-INSPIRE
Award Identifier / Grant number: IFA 12-MA-13
It is a great pleasure for the authors to thank Professor Peter Sarnak for his thoughtful comments on the paper. We also thank the School of Mathematics TIFR, Mumbai and the Department of Mathematics, IISc., Bangalore, where parts of this work was carried out, for providing excellent working atmosphere. The authors are grateful to the anonymous referee for a careful reading of the paper and for many helpful suggestions that improved the presentation.
Received: 2013-1-8
Revised: 2013-4-23
Published Online: 2015-7-5
Published in Print: 2015-7-1
© 2015 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Notes on occupation time fluctuations of binary branching particle systems
- On the sum of two integral squares in certain quadratic fields
- A Cesàro average of Goldbach numbers
- Groups described by element numbers
- The second main theorem for entire curves into Hilbert modular surfaces
- L∞ norms of holomorphic modular forms in the case of compact quotient
- SU(2)-Donaldson invariants of the complex projective plane
- Pairs of diagonal quadratic forms and linear correlations among sums of two squares
- The subelliptic heat kernel on the three-dimensional solvable Lie groups
- Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels
- Circle-valued Morse theory for complex hyperplane arrangements
- Atomic Hp spaces and their duals on open subsets of ℝd
- Locally contractible coset spaces
- L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups
- Finite time blow-up for semilinear wave equations with variable coefficients
- Intertwining operators of irreducible representations for exponential solvable Lie groups
- Artin's conjecture and systems of diagonal equations
- The homology of simplicial complements and the cohomology of polyhedral products
- Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator
- Multilinear generalized Radon transforms and point configurations
- On ratios of Petersson norms for Yoshida lifts
- K-groups for rings of finite Cohen–Macaulay type
- Character degree sums of finite groups
- Tame Fréchet submanifolds of co-Banach type
- Weighted norm inequalities for Schrödinger type operators
Artikel in diesem Heft
- Frontmatter
- Notes on occupation time fluctuations of binary branching particle systems
- On the sum of two integral squares in certain quadratic fields
- A Cesàro average of Goldbach numbers
- Groups described by element numbers
- The second main theorem for entire curves into Hilbert modular surfaces
- L∞ norms of holomorphic modular forms in the case of compact quotient
- SU(2)-Donaldson invariants of the complex projective plane
- Pairs of diagonal quadratic forms and linear correlations among sums of two squares
- The subelliptic heat kernel on the three-dimensional solvable Lie groups
- Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels
- Circle-valued Morse theory for complex hyperplane arrangements
- Atomic Hp spaces and their duals on open subsets of ℝd
- Locally contractible coset spaces
- L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups
- Finite time blow-up for semilinear wave equations with variable coefficients
- Intertwining operators of irreducible representations for exponential solvable Lie groups
- Artin's conjecture and systems of diagonal equations
- The homology of simplicial complements and the cohomology of polyhedral products
- Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator
- Multilinear generalized Radon transforms and point configurations
- On ratios of Petersson norms for Yoshida lifts
- K-groups for rings of finite Cohen–Macaulay type
- Character degree sums of finite groups
- Tame Fréchet submanifolds of co-Banach type
- Weighted norm inequalities for Schrödinger type operators
