Analytical continuation of prime zeta function for $\Re(s)>\frac{1}{2}$ assuming (RH)
Number Theory
2026-03-31 v2
Abstract
We derive a simple expression to analytically continue the prime zeta function to the domain assuming (RH) and taking into account a proper branch cut. We also verify the formula numerically and provide several plots.
Keywords
Cite
@article{arxiv.2603.25076,
title = {Analytical continuation of prime zeta function for $\Re(s)>\frac{1}{2}$ assuming (RH)},
author = {Artur Kawalec},
journal= {arXiv preprint arXiv:2603.25076},
year = {2026}
}
Comments
5 pages, 3 figures