Short Second Moment Bound for GL(2) $L$-functions in $q$-Aspect
Number Theory
2025-05-27 v3
Abstract
We prove a Lindel\"{o}f-on-average upper bound for the second moment of the -functions associated to a level 1 holomorphic cusp form, twisted along a coset of subgroup of the characters modulo (where for some odd prime ). This result should be seen as a -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.
Keywords
Cite
@article{arxiv.2309.14593,
title = {Short Second Moment Bound for GL(2) $L$-functions in $q$-Aspect},
author = {Agniva Dasgupta},
journal= {arXiv preprint arXiv:2309.14593},
year = {2025}
}
Comments
Final Version. Minor revisions to incorporate suggestions from the referee. Added a sketch for higher prime powers