Series expansions for the Riemann zeta function
Number Theory
2024-04-18 v2 Complex Variables
Abstract
We prove a general result on representing the Riemann zeta function as a convergent infinite series in a complex vertical strip containing the critical line. We use this result to re-derive known expansions as well as to discover new series representations of the Riemann zeta function in terms of the incomplete gamma functions, generalized hypergeometric functions and Meijer -functions.
Cite
@article{arxiv.2312.03261,
title = {Series expansions for the Riemann zeta function},
author = {Alexey Kuznetsov},
journal= {arXiv preprint arXiv:2312.03261},
year = {2024}
}
Comments
10 pages (in this version some typos are fixed and two references are added)