descriptionPublicationkeyboard_double_arrow_right Article , Preprint 17 Sep 2022Embargo end date: 01 Jan 2022 English Publisher:Springer Science and Business Media LLCJournal:Research in Number Theory, volume 8 (issn: 2522-0160, eissn: 2363-9555,

Authors: D. A. Goldston; Ade Irma Suriajaya;

doi: 10.1007/s40993-022-00371-4 , 10.48550/arxiv.2205.06503

arXiv: http://arxiv.org/abs/2205.06503

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

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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.

9 pages

Related Organizations

California State University System
United States
San Jose State University
United States
Kyushu University
Japan

Keywords

Mathematics - Number Theory, FOS: Mathematics, 11M06, 11M26, 11N05, Number Theory (math.NT)

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