Irrationality of the Zeta Constants

Abstract

A general technique for proving the irrationality of the zeta constants $\zeta (s)$ for odd $s=2n+1\ge 3$ 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 $n\ge 1$, and $\zeta (3)$ are well known, but the results on the irrationality for the zeta constants $\zeta (2n+1)$, where $n\ge 2$, are new, and these results seem to confirm that these constants are irrational numbers.

Twenty Seven Pages. Keyword: Irrational number, Transcendental number, Beta constant, Zeta constant, Uniform distribution

References in corpus (1)

• A rapidly converging Ramanujan-type series for Catalan's constant