Two hypergeometric tales and a new irrationality measure of $\zeta (2)$

Abstract

We prove the new upper bound 5.095412 for the irrationality exponent of $\zeta (2)={\pi }^2/6$; the earlier record bound 5.441243 was established in 1996 by G. Rhin and C. Viola.

17 pages

References in corpus (1)

• On simultaneous diophantine approximations to $\zeta (2)$ and $\zeta (3)$

Cited by in corpus (5)

• Irrationality proofs for zeta values, moduli spaces and dinner parties
• Hypergeometric rational approximations to $\zeta (4)$
• On simultaneous diophantine approximations to $\zeta (2)$ and $\zeta (3)$
• Vectors of type II Hermite-Padé approximations and a new linear independence criterion
• On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums