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In this paper, we focus on a q-analogue of the Riemann zeta function atpositive integers, which can be written for s\in\N^* by \zeta_q(s)=\sum_{k\geq1}q^k\sum_{d|k}d^{s-1}. We give a new lower bound for the dimension of thevector space over \Q spanned, for 1/q\in\Z\setminus\{-1;1\} and an even integerA, by 1,\zeta_q(3),\zeta_q(5),...,\zeta_q(A-1). This improves a recent resultof Krattenthaler, Rivoal and Zudilin (\emph{S\'eries hyperg\'eom\'etriquesbasiques, q-analogues des valeurs de la fonction zeta et s\'eriesd'Eisenstein}, J. Inst. Jussieu {\bf 5}.1 (2006), 53-79). In particular, aconsequence of our result is that for 1/q\in\Z\setminus\{-1;1\}, at least oneof the numbers \zeta_q(3),\zeta_q(5),\zeta_q(7),\zeta_q(9) is irrational.

Irrationalit\'e aux entiers impairs positifs d'un q-analogue de la fonction zeta de Riemann