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arXiv · 2007.16099

A singular series average and the zeros of the Riemann zeta-function

D. A. Goldston·Ade Irma Suriajaya
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Abstract

We show that the Riesz mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures has an asymptotic formula with an error term that can be expressed as an explicit formula that depends on the zeros of the Riemann zeta-function. Unconditionally this error term can be shown to oscillate, while conditionally it can be shown to oscillate between sharp bounds.

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BibTeXRIS

D. A. Goldston, Ade Irma Suriajaya. 2020-07-31. A singular series average and the zeros of the Riemann zeta-function. https://doi.org/10.4064/aa200821-24-2

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