La Zeta de Riemann est irrationnelle aux impairs positifs

Abstract

We found, by Hurwitz's Zeta Function, a new functional equation for Riemann Zeta Function. Considering this equation for $s=2$ and $s=1$, we determine a relation between the values of Riemann zeta Function on positive integers. The Matrix has two dimensions, and the second member is the vector (1, $-\zeta(2)$). The elements of this vector are linearly independent on the Rationals; and from this independence, we determined that $\zeta(j)$ is irrational for each j=3,4,5,6,7,8,9,....