An explicit sub-Weyl bound for $\zeta(1/2 + it)$

Dhir Patel; Andrew Yang

An explicit sub-Weyl bound for $\zeta(1/2 + it)$

Number Theory 2023-02-28 v1

Authors: Dhir Patel , Andrew Yang

Abstract

In this article we prove an explicit sub-Weyl bound for the Riemann zeta function $\zeta(s)$ on the critical line $s = 1/2 + it$ . In particular, we show that $|\zeta(1/2 + it)| \le 66.7\, t^{27/164}$ for $t \ge 3$ . Combined, our results form the sharpest known bounds on $\zeta(1/2 + it)$ for $t \ge \exp(61)$ .

Keywords

riemann zeta function zeta values and euler sums zeta functions

Cite

@article{arxiv.2302.13444,
  title  = {An explicit sub-Weyl bound for $\zeta(1/2 + it)$},
  author = {Dhir Patel and Andrew Yang},
  journal= {arXiv preprint arXiv:2302.13444},
  year   = {2023}
}

Comments

30 pages

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