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arXiv · 2109.12495

Mixed Moments of the Riemann Zeta and Dirichlet $L$-Functions

Ikuya Kaneko
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Abstract

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.

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Ikuya Kaneko. 2023-11-21. Mixed Moments of the Riemann Zeta and Dirichlet $L$-Functions. https://doi.org/10.1007/s00209-024-03657-8

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