The Zeta Quotient $\zeta(3)/ \pi^3$ is Irrational

N. A. Carella

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arXiv · 1906.10618

The Zeta Quotient $\zeta(3)/ \pi^3$ is Irrational

N. A. Carella

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Abstract

This note proves that the first odd zeta value does not have a closed form formula $\zeta(3)\ne r \pi^3$ for any rational number $r \in \mathbb{Q}$. Furthermore, assuming the irrationality of the second odd zeta value $\zeta(5)$, it is shown that $\zeta(5)\ne r\pi^5$ for any rational number $r \in \mathbb{Q}$.

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N. A. Carella. 2019-06-18. The Zeta Quotient $\zeta(3)/ \pi^3$ is Irrational. https://arxiv.org/abs/1906.10618

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