Meromorphic Continuation of the Goldbach generating function

TL;DR

This paper studies the Dirichlet series linked to representing integers as sums of primes, extending its domain of meromorphic continuation under the Riemann hypothesis.

Contribution

It establishes the domain of meromorphic continuation for the Goldbach generating function assuming the Riemann hypothesis.

Findings

Meromorphic continuation domain determined under RH

Conditional on Riemann hypothesis

Advances understanding of Goldbach representations

Abstract

We consider the Dirichlet series associated to the number of representations of an integer as the sum of primes. Assuming the Riemann hypothesis on the distribution of the zeros of the Riemann zeta function we obtain the domain of meromorphic continuation of this series.