Strong Hybrid Subconvexity for Twisted Selfdual $\mathrm{GL}_3$ $L$-Functions
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910208311164928 |
|---|---|
| author | Ganguly, Soumendra Humphries, Peter Lin, Yongxiao Nunes, Ramon |
| author_facet | Ganguly, Soumendra Humphries, Peter Lin, Yongxiao Nunes, Ramon |
| contents | We prove strong hybrid subconvex bounds simultaneously in the $q$ and $t$ aspects for $L$-functions of selfdual $\mathrm{GL}_3$ cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds for central values of certain $\mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions. The subconvex bounds that we obtain are strong in the sense that, modulo current knowledge on estimates for the second moment of $\mathrm{GL}_3$ $L$-functions, they are the natural limit of the first moment method pioneered by Li and by Blomer.
The method of proof relies on an explicit $\mathrm{GL}_3 \times \mathrm{GL}_2 \leftrightsquigarrow \mathrm{GL}_4 \times \mathrm{GL}_1$ spectral reciprocity formula, which relates a $\mathrm{GL}_2$ moment of $\mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions to a $\mathrm{GL}_1$ moment of $\mathrm{GL}_4 \times \mathrm{GL}_1$ Rankin-Selberg $L$-functions. A key additional input is a Lindelöf-on-average upper bound for the second moment of Dirichlet $L$-functions restricted to a coset, which is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong Hybrid Subconvexity for Twisted Selfdual $\mathrm{GL}_3$ $L$-Functions Ganguly, Soumendra Humphries, Peter Lin, Yongxiao Nunes, Ramon Number Theory 11F67 (primary), 11F12, 11F66 (secondary) We prove strong hybrid subconvex bounds simultaneously in the $q$ and $t$ aspects for $L$-functions of selfdual $\mathrm{GL}_3$ cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds for central values of certain $\mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions. The subconvex bounds that we obtain are strong in the sense that, modulo current knowledge on estimates for the second moment of $\mathrm{GL}_3$ $L$-functions, they are the natural limit of the first moment method pioneered by Li and by Blomer. The method of proof relies on an explicit $\mathrm{GL}_3 \times \mathrm{GL}_2 \leftrightsquigarrow \mathrm{GL}_4 \times \mathrm{GL}_1$ spectral reciprocity formula, which relates a $\mathrm{GL}_2$ moment of $\mathrm{GL}_3 \times \mathrm{GL}_2$ Rankin-Selberg $L$-functions to a $\mathrm{GL}_1$ moment of $\mathrm{GL}_4 \times \mathrm{GL}_1$ Rankin-Selberg $L$-functions. A key additional input is a Lindelöf-on-average upper bound for the second moment of Dirichlet $L$-functions restricted to a coset, which is of independent interest. |
| title | Strong Hybrid Subconvexity for Twisted Selfdual $\mathrm{GL}_3$ $L$-Functions |
| topic | Number Theory 11F67 (primary), 11F12, 11F66 (secondary) |
| url | https://arxiv.org/abs/2408.00596 |