The Mangoldt function and the non-trivial zeros of the Riemann zeta function

Abstract

We prove a formula for the Mangoldt function which relates it to a sum over all the non-trivial zeros of the Riemann zeta function, in addition we analize a truncated version of it.

15 pages. We have added a new formula for the spectrum of the prime numbers

References in corpus (1)

• Approximation of Riemann's zeta function by finite Dirichlet series: multiprecision numerical approach