On an Average Goldbach Representation Formula of Fujii

Fujii obtained a formula for the average number of Goldbach representations with lower order terms expressed as a sum over the zeros of the Riemann zeta-function and a smaller error term. This assumed the Riemann Hypothesis. We obtain an unconditional version of this result, and obtain applications...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Goldston, D A, Ade, Irma Suriajaya
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 20.12.2022
Subjects:	Representations
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	Fujii obtained a formula for the average number of Goldbach representations with lower order terms expressed as a sum over the zeros of the Riemann zeta-function and a smaller error term. This assumed the Riemann Hypothesis. We obtain an unconditional version of this result, and obtain applications conditional on various conjectures on zeros of the Riemann zeta-function.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2110.14250