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.

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