Hypergeometry inspired by irrationality questions

Abstract

We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log 2$, and ${\pi }^2$, their connection with already known ones, and underlying "permutation group" structures. Our principal arithmetic achievement is a new partial irrationality result for the values of Riemann's zeta function at odd integers.

AmS-LaTeX, 15 pages

References in corpus (3)

• A few remarks on linear forms involving Catalan's constant
• One of the Odd Zeta Values from $\zeta (5)$ to $\zeta (25)$ Is Irrational. By Elementary Means
• A note on odd zeta values

Cited by in corpus (5)

• Many odd zeta values are irrational
• One of the Odd Zeta Values from $\zeta (5)$ to $\zeta (25)$ Is Irrational. By Elementary Means
• A note on odd zeta values
• Hypergeometric rational approximations to $\zeta (4)$
• Arithmetic of Catalan's constant and its relatives