# On a smoothed average of the number of Goldbach representations

Source: [On a smoothed average of the number of Goldbach representations](<https://www.sota2.com/research/paper/68fa5c191e209131ce9ce239>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:26:27.186Z

Authors: Daniel A. Goldston, Ade Irma Suriajaya

Published: 2023-06-07T22:07:02.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2306.04807>)

[PDF](<https://arxiv.org/pdf/2306.04807.pdf>)