Explicit estimates for $\zeta(s)$ in the critical strip under the Riemann Hypothesis

Aleksander Simonič

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arXiv · 2109.11744

Explicit estimates for $\zeta(s)$ in the critical strip under the Riemann Hypothesis

Aleksander Simonič

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Abstract

Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for $\left|\zeta(s)\right|$ right to the critical line. As an application we make explicit Titchmarsh's conditional bound for the Mertens function and Montgomery--Vaughan's conditional bound for the number of $k$-free numbers.

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Aleksander Simonič. 2021-09-24. Explicit estimates for $\zeta(s)$ in the critical strip under the Riemann Hypothesis. https://arxiv.org/abs/2109.11744

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