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arXiv · 2010.13307

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

Aleksander Simonič
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Abstract

Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S(t)$, $S_1(t)$, and $ζ\left(1/2+\mathrm{i}t\right)$ 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.

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Aleksander Simonič. 2021-10-13. On explicit estimates for $S(t)$, $S_1(t)$, and $ζ(1/2+\mathrm{i}t)$ under the Riemann Hypothesis. https://doi.org/10.1016/j.jnt.2021.05.014

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