Hypergeometry inspired by irrationality questions

TL;DR

This paper introduces new hypergeometric methods for approximating mathematical constants like Catalan's constant, log 2, and pi squared, revealing permutation group structures and advancing irrationality results for zeta at odd integers.

Contribution

It presents novel hypergeometric constructions for rational approximations and establishes a new partial irrationality result for zeta function values at odd integers.

Findings

New hypergeometric constructions for constants

Connection with known approximation methods

Partial irrationality results for zeta at odd integers

Abstract

We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, 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.