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

D. A. Goldston, Ade Irma Suriajaya

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number71
JournalResearch in Number Theory
Volume8
Issue number4
DOIs
Publication statusPublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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