The prime number theorem and pair correlation of zeros of the Riemann zeta-function

We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery’s conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in long ranges and with suitable error terms.

Bibliographic Details

Published in:	Research in number theory Vol. 8; no. 4
Main Authors:	Goldston, D. A., Suriajaya, Ade Irma
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.12.2022 Springer Nature B.V
Subjects:	Mathematics Mathematics and Statistics Number Theory Prime numbers Theorems 11M26 Prime numbers 11M06 11N05 Riemann zeta-function Prime number theorem
ISSN:	2522-0160, 2363-9555
Online Access:	Get full text
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