On a Smoothed Average of the Number of Goldbach Representations

Daniel A. Goldston () and Ade Irma Suriajaya ()
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Daniel A. Goldston: San Jose State University, Department of Mathematics and Statistics
Ade Irma Suriajaya: Kyushu University, Faculty of Mathematics

A chapter in Number Theory in Memory of Eduard Wirsing, 2023, pp 145-156 from Springer

Abstract: 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 [11, 12] but without any smoothing factor. In this short article, we also show how the smoothing can be removed.

Keywords: Goldbach conjecture; L-function; Riemann zeta-function; Non-trivial zero (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-31617-3_10

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DOI: 10.1007/978-3-031-31617-3_10

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