On explicit estimates for $S(t)$, $S_1(t)$, and $ζ(1/2+\mathrm{i}t)$ under the Riemann Hypothesis

Aleksander Simonič

doi:10.1016/j.jnt.2021.05.014

paper

On explicit estimates for $S (t)$ , $S_{1} (t)$ , and $ζ (1/2 + i t)$ under the Riemann Hypothesis

arXiv:2010.13307 · doi:10.1016/j.jnt.2021.05.014

Abstract

Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S (t)$ , $S_{1} (t)$ , and $ζ (1/2 + i t)$ while comparing them with recently proven unconditional ones. As a corollary we obtain a conditional explicit bound on gaps between consecutive zeros of the Riemann zeta-function.

21 pages

On explicit estimates for S(t), S1​(t), and ζ(1/2+it) under the Riemann Hypothesis

Abstract

On explicit estimates for $S (t)$ , $S_{1} (t)$ , and $ζ (1/2 + i t)$ under the Riemann Hypothesis