Beukers-like proofs of irrationality for $\zeta (2)$ and $\zeta (3)$

Abstract

In this note, I develop step-by-step proofs of irrationality for $\zeta (2)$ and $\zeta (3)$. Though the proofs follow closely those based upon unit-square integrals proposed originally by Beukers, I introduce some modifications which certainly will be useful for those interested in understanding this kind of proof and/or trying to extend it to higher zeta values, Catalan's constant, or other related numbers.

A few corrections in the text and footnotes. New footnotes. Two additional references. Elsevier document class updated. 13 pages, no figures