Irrationalité aux entiers impairs positifs d'un q-analogue de la fonction zeta de Riemann
| dc.creator | Jouhet, Frederic | |
| dc.creator | Mosaki, Elie | |
| dc.date | 2007-12-11 | |
| dc.date.accessioned | 2026-07-07T08:48:36Z | |
| dc.date.available | 2026-07-07T08:48:36Z | |
| dc.description | In this paper, we focus on a q-analogue of the Riemann zeta function at positive integers, which can be written for s\in\N^* by ζ_q(s)=\sum_{k\geq 1}q^k\sum_{d|k}d^{s-1}. We give a new lower bound for the dimension of the vector space over \Q spanned, for 1/q\in\Z\setminus\{-1;1\} and an even integer A, by 1,ζ_q(3),ζ_q(5),...,ζ_q(A-1). This improves a recent result of Krattenthaler, Rivoal and Zudilin (\emph{Séries hypergéométriques basiques, q-analogues des valeurs de la fonction zeta et séries d'Eisenstein}, J. Inst. Jussieu {\bf 5}.1 (2006), 53-79). In particular, a consequence of our result is that for 1/q\in\Z\setminus\{-1;1\}, at least one of the numbers ζ_q(3),ζ_q(5),ζ_q(7),ζ_q(9) is irrational. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/0712.1762 | |
| dc.identifier | http://arxiv.org/abs/0712.1762 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144004 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11J72 (Primary); 33D15 (Secondary) | |
| dc.title | Irrationalité aux entiers impairs positifs d'un q-analogue de la fonction zeta de Riemann | |
| dc.type | text |