On a smoothed average of the number of Goldbach representations

Abstract

Assuming the Generalized Riemann Hypothesis for the zeros of the Dirichlet $L$-functions with characters modulo $q$, we obtain a smoothed version of the average number of Goldbach representations for numbers which are multiples of a positive integer $q$. Such an average was first considered by Granville \cite{Gran07,Gran08} but without any smoothing factor. In this short article, we also show how the smoothing can be removed.

Dedicated to the memory of Eduard Wirsing, 8 pages

References in corpus (1)

• On an Average Goldbach Representation Formula of Fujii

Cited by in corpus (2)

• The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function
• The average number of Goldbach representations over multiples of $q$