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:	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:	Prime numbers Theorems
ISSN:	2331-8422
Online Access:	Get full text
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