Simple bounds for the auxiliary function of Riemann
Abstract
We give simple numerical bounds for $\zeta(s)$, $\vartheta(s)$, $\mathop{\mathcal R}(s)$, $Z(t)$, for use in the numerical computation of these functions. The purpose of the paper is to give bounds for several functions needed in the calculation of $\zeta(s)$ and $Z(t)$. We are not pretending to have any originality. Our object is to be useful as a reference in our work for simple (simple to compute and simple to check) bounds.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.06681
- arXiv:
- arXiv:2407.06681
- Bibcode:
- 2024arXiv240706681A
- Keywords:
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- Mathematics - Number Theory;
- Primary 11M06;
- Secondary 30D99
- E-Print:
- 8 pages