# The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function

Source: [The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function](<https://www.sota2.com/research/paper/68fa59e41e209131ce9bb176>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T16:10:46.047Z

Authors: D. A. Goldston, Ade Irma Suriajaya

Published: 2022-05-13T08:22:38.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2205.06503>)

[PDF](<https://arxiv.org/pdf/2205.06503.pdf>)