Short Second Moment Bound for GL(2) $L$-functions in $q$-Aspect

Fuente: arXiv
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Main Author: Dasgupta, Agniva
Format: Preprint
Published: 2023
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author Dasgupta, Agniva
author_facet Dasgupta, Agniva
contents We prove a Lindelöf-on-average upper bound for the second moment of the $L$-functions associated to a level 1 holomorphic cusp form, twisted along a coset of subgroup of the characters modulo $q^{2/3}$ (where $q = p^3$ for some odd prime $p$). This result should be seen as a $q$-aspect analogue of Anton Good's (1982) result on upper bounds of the second moment of cusp forms in short intervals. The results generalize easily to higher prime powers as well.
format Preprint
id arxiv_https___arxiv_org_abs_2309_14593
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Short Second Moment Bound for GL(2) $L$-functions in $q$-Aspect
Dasgupta, Agniva
Number Theory
11M06 (Primary) 11F11, 11F12, 11F66 (Secondary)
We prove a Lindelöf-on-average upper bound for the second moment of the $L$-functions associated to a level 1 holomorphic cusp form, twisted along a coset of subgroup of the characters modulo $q^{2/3}$ (where $q = p^3$ for some odd prime $p$). This result should be seen as a $q$-aspect analogue of Anton Good's (1982) result on upper bounds of the second moment of cusp forms in short intervals. The results generalize easily to higher prime powers as well.
title Short Second Moment Bound for GL(2) $L$-functions in $q$-Aspect
topic Number Theory
11M06 (Primary) 11F11, 11F12, 11F66 (Secondary)
url https://arxiv.org/abs/2309.14593