English

An improved explicit estimate for $\zeta(1/2+it)$

Number Theory 2022-07-07 v1

Abstract

An explicit subconvex bound for the Riemann zeta function ζ(s)\zeta(s) on the critical line s=1/2+its=1/2+it is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-Landau lemma. After accounting for the needed correction in that lemma, we recover and improve the record explicit bound for ζ(1/2+it)|\zeta(1/2 + it)|.

Keywords

Cite

@article{arxiv.2207.02366,
  title  = {An improved explicit estimate for $\zeta(1/2+it)$},
  author = {Ghaith A. Hiary and Dhir Patel and Andrew Yang},
  journal= {arXiv preprint arXiv:2207.02366},
  year   = {2022}
}

Comments

19 pages

R2 v1 2026-06-24T12:15:13.427Z