Arithmetic of linear forms involving odd zeta values

A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of $\zeta (2)$ and $\zeta (3)$, as well as to explain Rivoal’s “infinitely-many” result (math.NT/0008051) and to prove that at least one of the four numbers $\zeta (5)$, $\zeta (7)$, $\zeta (9)$, and $\zeta (11)$ is irrational.