Short Second Moment Bound for GL(2) $L$-functions in $q$-Aspect
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908376779194368 |
|---|---|
| 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 |