New bounds for $\psi(x)$
Number Theory
2019-03-06 v1
Abstract
In this article we provide new explicit Chebyshev's bounds for the prime counting function . The proof relies on two new arguments: smoothing the prime counting function which allows to generalize the previous approaches, and a new explicit zero density estimate for the zeros of the Riemann zeta function.
Cite
@article{arxiv.1310.6374,
title = {New bounds for $\psi(x)$},
author = {Laura Faber and Habiba Kadiri},
journal= {arXiv preprint arXiv:1310.6374},
year = {2019}
}
Comments
19 pages, to appear in Mathematics of Computation