First moment of central values of quadratic Dirichlet $L$-functions

Peng Gao; Liangyi Zhao

First moment of central values of quadratic Dirichlet $L$-functions

Number Theory 2024-08-27 v4

Authors: Peng Gao , Liangyi Zhao

Abstract

We evaluate the first moment of central values of the family of quadratic Dirichlet $L$ -functions using the method of double Dirichlet series. Under the generalized Riemann hypothesis, we prove an asymptotic formula with an error term of size that is the fourth root of that of the primary main term.

Keywords

quadratic dirichlet l-functions central values first moment double dirichlet series generalized riemann hypothesis asymptotic formula

Cite

@article{arxiv.2303.11588,
  title  = {First moment of central values of quadratic Dirichlet $L$-functions},
  author = {Peng Gao and Liangyi Zhao},
  journal= {arXiv preprint arXiv:2303.11588},
  year   = {2024}
}

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11 pages

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