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.

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Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org
Hauptverfasser:	Goldston, D A, Ade, Irma Suriajaya
Format:	Paper
Sprache:	Englisch
Veröffentlicht:	Ithaca Cornell University Library, arXiv.org 20.12.2022
Schlagworte:	Prime numbers Theorems
ISSN:	2331-8422
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
Bibliographie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2205.06503