  The knowledge on irrationality of p-adic zeta values has recently progressed.
The irrationality of zeta_2(2), \zeta_2(3) and of a few other p-adic series of
Dirichlet was obtained by F. Calegari. F. Beukers gave a more elementary proof
of this result. In parallel, T. Rivoal has just obtained, in the complex case,
some Pade approximants of Lerch functions. It is this work which, transposed to
C_p, enables us to obtain results of irrationality and linear independence.
