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arXiv · 2306.04807

On a smoothed average of the number of Goldbach representations

Daniel A. Goldston·Ade Irma Suriajaya
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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.

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Daniel A. Goldston, Ade Irma Suriajaya. 2023-06-07. On a smoothed average of the number of Goldbach representations. https://doi.org/10.1007/978-3-031-31617-3_10

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