On sup-norms of cusp forms of powerful level

Abhishek Saha

doi:10.4171/JEMS/746

On sup-norms of cusp forms of powerful level

Abhishek Saha

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue \lambda. It is shown that |f|_\infty 0. The exponent is further improved in the case when N is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of N squarefree.

Original language	English
Pages (from-to)	3549-3573
Number of pages	25
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	11
DOIs	https://doi.org/10.4171/JEMS/746
Publication status	Published - 3 Oct 2017

Keywords

Maass form
Sup-norm
Fourier coefficients
Amplification

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10.4171/JEMS/746

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via EMS at http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=19&iss=11&rank=8&srch=searchterm%7CSaha. Please refer to any applicable terms of use of the publisher.
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title = "On sup-norms of cusp forms of powerful level",

abstract = "Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue \lambda. It is shown that |f|_\infty 0. The exponent is further improved in the case when N is not divisible by {"}small squares{"}. Our work extends and generalizes previously known results in the special case of N squarefree.",

keywords = "Maass form, Sup-norm, Fourier coefficients, Amplification",

author = "Abhishek Saha",

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TY - JOUR

T1 - On sup-norms of cusp forms of powerful level

AU - Saha, Abhishek

PY - 2017/10/3

Y1 - 2017/10/3

N2 - Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue \lambda. It is shown that |f|_\infty 0. The exponent is further improved in the case when N is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of N squarefree.

AB - Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue \lambda. It is shown that |f|_\infty 0. The exponent is further improved in the case when N is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of N squarefree.

KW - Maass form

KW - Sup-norm

KW - Fourier coefficients

KW - Amplification

UR - https://arxiv.org/abs/1404.3179

U2 - 10.4171/JEMS/746

DO - 10.4171/JEMS/746

M3 - Article (Academic Journal)

SN - 1435-9855

VL - 19

SP - 3549

EP - 3573

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 11

ER -

On sup-norms of cusp forms of powerful level

Abstract

Keywords

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Arithmetic aspects of automorphic forms: Petersson norms and special values of L-functions.

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On sup-norms of cusp forms of powerful level

Abstract

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Arithmetic aspects of automorphic forms: Petersson norms and special values of L-functions.

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