English

Oscillations of the error term in the prime number theorem

Number Theory 2019-12-03 v1

Abstract

Let σ+iγ\sigma+i\gamma be a zero of the Riemann zeta function to the right of the line 12+it\frac{1}{2}+it. We show that this zero causes large oscillations of the error term of the prime number theorem. Our result is close to optimal both in terms of the magnitude and in the localization of large values for the error term.

Keywords

Cite

@article{arxiv.1912.00853,
  title  = {Oscillations of the error term in the prime number theorem},
  author = {Jan-Christoph Schlage-Puchta},
  journal= {arXiv preprint arXiv:1912.00853},
  year   = {2019}
}