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

TL;DR

The paper derives an explicit formula to extend the prime zeta function analytically for real part greater than 1/2, assuming the Riemann Hypothesis, and verifies it numerically.

Contribution

It provides a new explicit expression for the prime zeta function's analytic continuation under the Riemann Hypothesis, including numerical verification.

Findings

Derived a simple explicit formula for the continuation.

Verified the formula numerically with several plots.

Assumed the Riemann Hypothesis for the derivation.

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.