A singular series average and the zeros of the Riemann zeta-function
Number Theory
2021-09-21 v1
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.
Keywords
Cite
@article{arxiv.2007.16099,
title = {A singular series average and the zeros of the Riemann zeta-function},
author = {D. A. Goldston and Ade Irma Suriajaya},
journal= {arXiv preprint arXiv:2007.16099},
year = {2021}
}
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14 pages