  In this paper we refine Ball-Rivoal's theorem by proving that for any odd
integer $a$ sufficiently large in terms of $\epsilon>0$, there exist $[
\frac{(1-\epsilon)\log a}{1+\log 2}]$ odd integers $s$ between 3 and $a$, with
distance at least $a^{\epsilon}$ from one another, at which Riemann zeta
function takes $\Q$-linearly independent values. As a consequence, if there are
very few integers $s$ such that $\zeta(s)$ is irrational, then they are rather
evenly distributed. The proof involves series of hypergeometric type estimated
by the saddle point method, and the generalization to vectors of Nesterenko's
linear independence criterion.
