Explicit estimates for $\zeta(s)$ in the critical strip under the Riemann Hypothesis
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.11744
- arXiv:
- arXiv:2109.11744
- Bibcode:
- 2021arXiv210911744S
- Keywords:
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- Mathematics - Number Theory;
- 11M26;
- 11N37;
- 11Y35
- E-Print:
- 24 pages, additional remarks