The error term in the prime number theorem
Number Theory
2020-07-21 v2
Abstract
We make explicit a theorem of Pintz concerning the error term in the prime number theorem. This gives an improved version of the prime number theorem with error term roughly square-root of that which was previously known. We apply this to a long-standing problem concerning an inequality studied by Ramanujan.
Cite
@article{arxiv.1809.03134,
title = {The error term in the prime number theorem},
author = {Dave Platt and Tim Trudgian},
journal= {arXiv preprint arXiv:1809.03134},
year = {2020}
}
Comments
To appear in Math. Comp