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

## TL;DR

This paper establishes a new formula connecting the Mangoldt function to the non-trivial zeros of the Riemann zeta function and analyzes a truncated version of this relationship.

## Contribution

It introduces a novel explicit formula linking the Mangoldt function with the zeros of the zeta function and explores its truncated form.

## Key findings

- Derived a formula relating the Mangoldt function to zeta zeros
- Analyzed the properties of a truncated version of the formula
- Provided insights into the distribution of zeta zeros

## 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.