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

Peng Gao; Liangyi Zhao

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

Number Theory 2025-04-04 v1

Authors: Peng Gao , Liangyi Zhao

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.

Keywords

l-functions moment problem function spaces and inequalities

Cite

@article{arxiv.2504.02225,
  title  = {Twisted second moment of modular $L$-functions to a fixed modulus},
  author = {Peng Gao and Liangyi Zhao},
  journal= {arXiv preprint arXiv:2504.02225},
  year   = {2025}
}

Comments

17 pages

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