The prime number theorem and pair correlation of zeros of the Riemann zeta-function
Research in Number Theory
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.
Japan Society for the Promotion of Science
Prime number theorem, Prime numbers, Riemann zeta-function
Mathematics and Statistics
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