# Hybrid sup-norm bounds for Hecke–Maass cusp forms

Journal of the European Mathematical Society (2015)

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

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topTemplier, 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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