Analytical continuation of prime zeta function for $\Re (s)>\frac{1}{2}$ assuming (RH)

Abstract

We derive a simple expression to analytically continue the prime zeta function to the domain $\Re (s)>\frac{1}{2}$ assuming (RH) and taking into account a proper branch cut. We also verify the formula numerically and provide several plots.

5 pages, 3 figures