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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Veröffentlicht in:Research in number theory Jg. 8; H. 4
Hauptverfasser: Goldston, D. A., Suriajaya, Ade Irma
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2022
Springer Nature B.V
Schlagworte:
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-Zugang:Volltext
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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:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-022-00371-4