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

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.

arXiv comment12 pages

References in corpus (7)

• The number of Goldbach representations of an integer
• Goldbach Representations in Arithmetic Progressions and zeros of Dirichlet L-functions
• A Cesàro Average of Goldbach numbers
• Sums of many primes
• On an Average Goldbach Representation Formula of Fujii
• The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function
• On a smoothed average of the number of Goldbach representations