# A geometrical summation method for the Riemann z\^eta function

## TL;DR

This paper presents a novel geometrical summation method that extends the convergence of the Riemann zeta function within the critical strip and offers a new perspective on its non-trivial zeros.

## Contribution

The paper introduces a geometrical summation technique that analytically continues the Riemann zeta function and proposes a new quantity potentially characterizing its non-trivial zeros.

## Key findings

- Method achieves convergence over the critical strip
- Introduces a new analytical function matching zeta
- Proposes a quantity related to non-trivial zeros

## Abstract

In this paper, we introduce a geometrical summation method that makes the original Riemann series converge over the critical strip. This method gives an analytical function, that coincides with z\^eta. This point of view allows us to introduce a quantity of interest that seems to give a characterization of the non-trivial zeros of the Riemann z\^eta function.