Arithmetic of Catalan's constant and its relatives

Abstract

We prove that at least one of the six numbers $\beta (2i)$ for $i=1,\dots ,6$ is irrational. Here $\beta (s)={\sum }_{k=0}^{\infty }(-1{)}^k(2k+1{)}^{-s}$ denotes Dirichlet's beta function, so that $\beta (2)$ is Catalan's constant.

9 pages

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Cited by in corpus (2)

• At least two of $\zeta (5),\zeta (7),\dots ,\zeta (35)$ are irrational
• Errata and Addenda to Mathematical Constants