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arXiv · 2504.02225

Twisted second moment of modular $L$-functions to a fixed modulus

Peng Gao·Liangyi Zhao
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Abstract

We study asymptotically the twisted second moment of the family of modular $L$-functions to a fixed modulus. As an application, we establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$ for the $2k$-th moment of these $L$-functions on the critical line.

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Peng Gao, Liangyi Zhao. 2025-04-03. Twisted second moment of modular $L$-functions to a fixed modulus. https://arxiv.org/abs/2504.02225

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