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

被引：0
作者：
D. A. Goldston
Ade Irma Suriajaya
机构：
[1] San Jose State University,Department of Mathematics and Statistics
[2] Kyushu University,Faculty of Mathematics
来源：
Research in Number Theory | 2022年 / 8卷
关键词：
Prime numbers; Riemann zeta-function; Prime number theorem; 11M06; 11M26; 11N05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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