English

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 (s)>12\Re(s)>\frac{1}{2} 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