New bounds for $\psi (x)$

Abstract

In this article we provide new explicit Chebyshev's bounds for the prime counting function $\psi (x)$. 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.

arXiv comment19 pages, to appear in Mathematics of Computation