Mixed Moments of the Riemann Zeta and Dirichlet $L$-Functions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915150754217984 |
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| author | Kaneko, Ikuya |
| author_facet | Kaneko, Ikuya |
| contents | We prove Motohashi's formula for a mixed second moment of the Riemann zeta function and a Dirichlet $L$-function attached to a primitive Dirichlet character modulo $q \in \mathbb{N}$. If $q$ is an odd prime, our reciprocity formula is consistent with Motohashi's result in the early 1990s. The cubic moment side features two versions of central $L$-values of automorphic forms on $Γ_{0}(q) \backslash \mathbb{H}$. The methods involve a blend of analytic number theory and automorphic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_12495 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Mixed Moments of the Riemann Zeta and Dirichlet $L$-Functions Kaneko, Ikuya Number Theory 11M06 (primary), 11F03, 11F72 (secondary) We prove Motohashi's formula for a mixed second moment of the Riemann zeta function and a Dirichlet $L$-function attached to a primitive Dirichlet character modulo $q \in \mathbb{N}$. If $q$ is an odd prime, our reciprocity formula is consistent with Motohashi's result in the early 1990s. The cubic moment side features two versions of central $L$-values of automorphic forms on $Γ_{0}(q) \backslash \mathbb{H}$. The methods involve a blend of analytic number theory and automorphic forms. |
| title | Mixed Moments of the Riemann Zeta and Dirichlet $L$-Functions |
| topic | Number Theory 11M06 (primary), 11F03, 11F72 (secondary) |
| url | https://arxiv.org/abs/2109.12495 |