The prime number theorem and pair correlation of zeros of the Riemann zeta-function
Publication Date
12-1-2022
Document Type
Article
Publication Title
Research in Number Theory
Volume
8
Issue
4
DOI
10.1007/s40993-022-00371-4
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.
Funding Number
18K13400
Funding Sponsor
Japan Society for the Promotion of Science
Keywords
Prime number theorem, Prime numbers, Riemann zeta-function
Department
Mathematics and Statistics
Recommended Citation
D. A. Goldston and Ade Irma Suriajaya. "The prime number theorem and pair correlation of zeros of the Riemann zeta-function" Research in Number Theory (2022). https://doi.org/10.1007/s40993-022-00371-4
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