Large values of quadratic Dirichlet $L$-functions near the central point

Zikang Dong; Zhonghua Li; Yutong Song; Shengbo Zhao

Large values of quadratic Dirichlet $L$-functions near the central point

Number Theory 2025-08-19 v1

Authors: Zikang Dong , Zhonghua Li , Yutong Song , Shengbo Zhao

Abstract

In this paper, we investigate the conditional large values of the quadratic Dirichlet $L$ -functions near the central point $s=1/2$ . When $\sigma$ closes to $1/2$ within a suitable range, we show that $L(\sigma, \chi_d)$ have the conditional large values of the similar order of magnitude as $L(1/2, \chi_d)$ .

Keywords

quadratic Dirichlet L-functions large values central point conditional estimates character sums

Cite

@article{arxiv.2508.12205,
  title  = {Large values of quadratic Dirichlet $L$-functions near the central point},
  author = {Zikang Dong and Zhonghua Li and Yutong Song and Shengbo Zhao},
  journal= {arXiv preprint arXiv:2508.12205},
  year   = {2025}
}

Related papers

View all related →