Extreme values of the real part of the Riemann zeta function

Qiyu Yang; Shengbo Zhao

Extreme values of the real part of the Riemann zeta function

Number Theory 2026-07-04 v1

Authors: Qiyu Yang , Shengbo Zhao

Abstract

In this paper, we establish lower bounds for extreme values of the real part of the Riemann zeta function on the critical line. This work relies on the resonance method of Bondarenko and Seip, together with lower bounds for certain integrals associated with Dirichlet series with non-negative coefficients. Our results extend the work of Bondarenko and Seip (2018).

Keywords

Riemann zeta function extreme values critical line resonance method Dirichlet series lower bounds

Cite

@article{arxiv.2607.03654,
  title  = {Extreme values of the real part of the Riemann zeta function},
  author = {Qiyu Yang and Shengbo Zhao},
  journal= {arXiv preprint arXiv:2607.03654},
  year   = {2026}
}