The average number of Goldbach representations over multiples of $q$

TL;DR

This paper improves estimates for the average number of Goldbach representations of integers that are multiples of q, building on Granville's work under the generalized Riemann hypothesis.

Contribution

It provides an improved estimate for the average Goldbach representations for multiples of q, extending Granville's previous results.

Findings

Enhanced bounds under the generalized Riemann hypothesis

Refined understanding of Goldbach representations for multiples of q

Advancement in analytic number theory techniques

Abstract

We discuss the evaluation of the average number of Goldbach representations for integers which are multiples of $q$ introduced by Granville. We improve an estimate given by Granville under the generalized Riemann hypothesis.