An elementary proof of Apery's theorem

Abstract

We present a new `elementary' proof of the irrationality of $\zeta (3)$ based on some recent `hypergeometric' ideas of Yu.Nesterenko, T.Rivoal, and K.Ball, and on Zeilberger's algorithm of creative telescoping.

8 pages

References in corpus (1)

• Irrationality of values of zeta-function

Cited by in corpus (6)

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Supercongruences for rigid hypergeometric Calabi--Yau threefolds
• Approximations to -, di- and tri- logarithms
• Well-poised generation of Apéry-like recursions
• Some Numeric Hypergeometric Supercongruences
• A single parameter Hermite-Padé series representations for Apéry's constant