On the error term in the explicit formula of Riemann--von Mangoldt
Number Theory
2024-01-09 v5
Abstract
We provide an explicit error term for the Riemann--von Mangoldt formula by making results of Wolke (1983) and Ramar\'e (2016) explicit. We also include applications to primes between consecutive powers, the error term in the prime number theorem and an inequality of Ramanujan.
Keywords
Cite
@article{arxiv.2111.10001,
title = {On the error term in the explicit formula of Riemann--von Mangoldt},
author = {Michaela Cully-Hugill and Daniel R. Johnston},
journal= {arXiv preprint arXiv:2111.10001},
year = {2024}
}
Comments
22 pages, corrections to references in the introduction