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arXiv · 2505.19375

Bounds for Moments of Dirichlet $L$-functions of fixed modulus on the critical line

Peng Gao·Liangyi Zhao
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Abstract

We study the $2k$-th moment of the family of Dirichlet $L$-functions to a fixed prime modulus on the critical line and establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$.

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Peng Gao, Liangyi Zhao. 2025-05-26. Bounds for Moments of Dirichlet $L$-functions of fixed modulus on the critical line. https://arxiv.org/abs/2505.19375

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