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

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.