A Hypergeometric Approach, Via Linear Forms Involving Logarithms, to Irrationality Criteria for Euler's Constant

Simple item page
dc.creatorSondow, Jonathan
dc.creatorZlobin, Sergey
dc.date2002-11-05
dc.date2009-04-29
dc.date.accessioned2026-07-07T13:09:29Z
dc.date.available2026-07-07T13:09:29Z
dc.descriptionUsing an integral of a hypergeometric function, we give necessary and sufficient conditions for irrationality of Euler's constant $γ$. The proof is by reduction to known irrationality criteria for $γ$ involving a Beukers-type double integral. We show that the hypergeometric and double integrals are equal by evaluating them. To do this, we introduce a construction of linear forms in 1, $γ$, and logarithms from Nesterenko-type series of rational functions. In the Appendix, Sergey Zlobin gives a change-of-variables proof that the series and the double integral are equal.
dc.descriptionTypos in statement of Lemma 2 corrected, reference [3] updated, published version. Appendix by Sergey Zlobin
dc.identifierhttps://arxiv.org/abs/math/0211075
dc.identifierhttp://arxiv.org/abs/math/0211075
dc.identifierMath. Slovaca 59 (2009), No. 3, 1-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228752
dc.subjectNumber Theory
dc.subjectClassical Analysis and ODEs
dc.subject11J72 (Primary) 11J86, 33C20 (Secondary)
dc.titleA Hypergeometric Approach, Via Linear Forms Involving Logarithms, to Irrationality Criteria for Euler's Constant
dc.typetext

Files

Collections

arXiv