Large values of the error term in the prime number theorem

TL;DR

This paper investigates the size of large error terms in the prime number theorem under the Riemann hypothesis, analyzing the zeros of the zeta function within Bohr sets to derive new estimates.

Contribution

It introduces novel estimates for large error terms in the prime number theorem by analyzing zeta zeros in Bohr sets, assuming the Riemann hypothesis.

Findings

New bounds for the size of large error term sets

Analysis of zeta zeros in Bohr sets

Enhanced understanding of error term fluctuations

Abstract

Assume the Riemann hypothesis throughout. We obtain some new estimates for the size of the set of large values of the error term in the prime number theorem. Our argument is based on an analysis of the behavior of zeros of the Riemann zeta function in Bohr sets.