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arXiv · 2610.41394

Twisted second moments of Dirichlet $L$-functions with applications to weighted one-level density

Naoto Inumaru·Shingo Sugiyama
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Abstract

We give an asymptotic formula for the twisted second moment of a fixed Dirichlet $L$-function in the $t$-aspect. This is a generalization of Selberg's asymptotic formula for the twisted second moment of the Riemann zeta function. As an application, we observe the change and the stability of the weighted one-level density of zeros of a fixed Dirichlet $L$-function.

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Naoto Inumaru, Shingo Sugiyama. 2026-10-30. Twisted second moments of Dirichlet $L$-functions with applications to weighted one-level density. https://arxiv.org/abs/2610.41394

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