Hybrid sup-norm bounds for Hecke–Maass cusp forms

Nicolas Templier

Journal of the European Mathematical Society (2015)

  • Volume: 017, Issue: 8, page 2069-2082
  • ISSN: 1435-9855

Abstract

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Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N . Normalize the hyperbolic measure such that vol ( Y 0 ( N ) ) = 1 and the form f such that ∥ f ∥ 2 = 1 . It is shown that ∥ f ∥ ∞ ≪ ϵ λ 5 24 + ϵ N 1 3 + ϵ for all ϵ > 0 . This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.

How to cite

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Templier, Nicolas. "Hybrid sup-norm bounds for Hecke–Maass cusp forms." Journal of the European Mathematical Society 017.8 (2015): 2069-2082. <http://eudml.org/doc/277432>.

@article{Templier2015,
abstract = {Let $f$ be a Hecke–Maass cusp form of eigenvalue $\lambda $ and square-free level $N$. Normalize the hyperbolic measure such that $\mathrm \{vol\}(Y_0(N))=1$ and the form $f$ such that $\Vert \{f\}\Vert _2=1$. It is shown that $\Vert \{f\}\Vert _\infty \ll _\epsilon \lambda ^\{\frac\{5\}\{24\}+\epsilon \} N^\{\frac\{1\}\{3\}+\epsilon \}$ for all $\epsilon >0$. This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.},
author = {Templier, Nicolas},
journal = {Journal of the European Mathematical Society},
keywords = {automorphic forms; trace formula; amplification; diophantine approximation; automorphic forms; trace formula; amplification; Diophantine approximation},
language = {eng},
number = {8},
pages = {2069-2082},
publisher = {European Mathematical Society Publishing House},
title = {Hybrid sup-norm bounds for Hecke–Maass cusp forms},
url = {http://eudml.org/doc/277432},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Templier, Nicolas
TI - Hybrid sup-norm bounds for Hecke–Maass cusp forms
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 8
SP - 2069
EP - 2082
AB - Let $f$ be a Hecke–Maass cusp form of eigenvalue $\lambda $ and square-free level $N$. Normalize the hyperbolic measure such that $\mathrm {vol}(Y_0(N))=1$ and the form $f$ such that $\Vert {f}\Vert _2=1$. It is shown that $\Vert {f}\Vert _\infty \ll _\epsilon \lambda ^{\frac{5}{24}+\epsilon } N^{\frac{1}{3}+\epsilon }$ for all $\epsilon >0$. This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.
LA - eng
KW - automorphic forms; trace formula; amplification; diophantine approximation; automorphic forms; trace formula; amplification; Diophantine approximation
UR - http://eudml.org/doc/277432
ER -

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