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arXiv · 2407.06681

Simple bounds for the auxiliary function of Riemann

Juan Arias de Reyna
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Abstract

We give simple numerical bounds for $ζ(s)$, $\vartheta(s)$, $\mathop{\mathcal R}(s)$, $Z(t)$, 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 $ζ(s)$ 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.

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Juan Arias de Reyna. 2024-07-09. Simple bounds for the auxiliary function of Riemann. https://arxiv.org/abs/2407.06681

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