On certain sums over primes and the Riesz function
Number Theory
2026-03-31 v1
Abstract
We offer some comments on series involving the Mbius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by applying Riemann-Stieltjes integration. We offer a new formula connecting the derivative of the Gram series to the Riesz function, which we then use to obtain general integral relationships.
Keywords
Cite
@article{arxiv.2508.13449,
title = {On certain sums over primes and the Riesz function},
author = {Alexander E. Patkowski},
journal= {arXiv preprint arXiv:2508.13449},
year = {2026}
}