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

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...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	arXiv.org
Hlavní autoři:	Goldston, D A, Ade, Irma Suriajaya
Médium:	Paper
Jazyk:	angličtina
Vydáno:	Ithaca Cornell University Library, arXiv.org 31.07.2020
ISSN:	2331-8422
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	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.
Bibliografie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2007.16099