English

On the error term in the explicit formula of Riemann-von Mangoldt II

Number Theory 2026-02-24 v3

Abstract

We give an explicit O(x/T)O(x/T) error term for the truncated Riemann--von Mangoldt explicit formula. For large xx, this provides a modest improvement over previous work, which we demonstrate via an application to a result on primes between consecutive powers.

Keywords

Cite

@article{arxiv.2402.04272,
  title  = {On the error term in the explicit formula of Riemann-von Mangoldt II},
  author = {Michaela Cully-Hugill and Daniel R. Johnston},
  journal= {arXiv preprint arXiv:2402.04272},
  year   = {2026}
}

Comments

19 pages, minor corrections