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arXiv · 1810.02361

La Zeta de Riemann est irrationnelle aux impairs positifs

Mundankulu Kabongo
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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,....

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Mundankulu Kabongo. 2018-10-04. La Zeta de Riemann est irrationnelle aux impairs positifs. https://arxiv.org/abs/1810.02361

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