The fourth moment of Dirichlet L-functions along the critical line

Xiaosheng Wu

The fourth moment of Dirichlet L-functions along the critical line

Number Theory 2022-10-14 v7

Authors: Xiaosheng Wu

Abstract

For a positive integer $q\not\equiv 2 \pmod 4$ , this work considers the fourth moment of Dirichlet $L$ -functions averaged over both $t\in [0,T]$ and primitive characters to modulus $q$ . An asymptotic formula with a power saving from both $q$ -aspect and $t$ -aspect in the error term is obtained.

Keywords

dirichlet l-functions fourth moment critical line primitive characters asymptotic formula power saving

Cite

@article{arxiv.2004.00504,
  title  = {The fourth moment of Dirichlet L-functions along the critical line},
  author = {Xiaosheng Wu},
  journal= {arXiv preprint arXiv:2004.00504},
  year   = {2022}
}

Comments

30 pages. any comments are welcome

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