Irrationality of the Zeta Constants

N. A. Carella

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arXiv · 1212.4082

Irrationality of the Zeta Constants

N. A. Carella

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Abstract

A general technique for proving the irrationality of the zeta constants $\zeta(s)$ for odd $s = 2n + 1 \geq 3$ from the known irrationality of the beta constants $L(2n+1)$ is developed in this note. The results on the irrationality of the zeta constants $\zeta(2n)$, where $n\geq 1$, and $\zeta(3)$ are well known, but the results on the irrationality for the zeta constants $\zeta(2n+1)$, where $n \geq 2$, are new, and these results seem to confirm that these constants are irrational numbers.

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BibTeX RIS

N. A. Carella. 2012-12-13. Irrationality of the Zeta Constants. https://arxiv.org/abs/1212.4082

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