Extreme values of derivatives of Dirichlet $L$-functions

Xinghua Cui; Zhifeng Peng; Yutong Song; Shengbo Zhao

Extreme values of derivatives of Dirichlet $L$-functions

Number Theory 2026-07-05 v1

Authors: Xinghua Cui , Zhifeng Peng , Yutong Song , Shengbo Zhao

Abstract

In this paper, we establish lower bounds for extreme values of derivatives of Dirichlet $L$ -functions in the range $1/2<\sigma<1$ . Compared with the work of Aistleitner, Mahatab, Munsch, and Peyrot in 2019, our result shows that derivatives of Dirichlet $L$ -functions can attain extreme values of the same order of magnitude as the original $L$ -functions when $1/2<\sigma<1$ holds.

Keywords

Dirichlet L-functions extreme values derivatives lower bounds critical strip

Cite

@article{arxiv.2607.04084,
  title  = {Extreme values of derivatives of Dirichlet $L$-functions},
  author = {Xinghua Cui and Zhifeng Peng and Yutong Song and Shengbo Zhao},
  journal= {arXiv preprint arXiv:2607.04084},
  year   = {2026}
}