A smooth version of Landaus explicit formula
Number Theory
2023-11-09 v1
Abstract
We present a smooth version of Landaus explicit formula for the von Mangoldt arithmetical function. Assuming the validity of the Riemann hypothesis, we show that in order to determine whether a natural number is a prime number, it is sufficient to know the location of a number of non trivial zeros of the Riemann zeta function. Next we use Heisenbergs inequality to support the conjecture that this number of zeros cannot be essentially diminished
Keywords
Cite
@article{arxiv.2311.04347,
title = {A smooth version of Landaus explicit formula},
author = {Eugenio P. Balanzario and Daniel Eduardo Cardenas Romero and Richar Chacon Serna},
journal= {arXiv preprint arXiv:2311.04347},
year = {2023}
}
Comments
21 pages with 1 figures