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arXiv · 1809.09440

Relations among the Riemann zeta and Hurwitz zeta functions as well as their products

A. C. L. Ashton·A. S. Fokas
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Abstract

Several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation if the important results of [11]. Also, a relation derived here provides the starting point of a novel approach which in a series of companion papers yields a formal proof of the Lindel\"{o}f hypothesis. Some of the above relations motivate the need for analysing the large $\alpha$ behaviour of the modified Hurwitz zeta function $\zeta_1(s,\alpha)$, $s\in \mathbf{C}$, $\alpha\in \mathbf{R}$, which is also presented here.

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A. C. L. Ashton, A. S. Fokas. 2018-09-25. Relations among the Riemann zeta and Hurwitz zeta functions as well as their products. https://arxiv.org/abs/1809.09440

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