Fonction Zêta de Hurwitz p-adique et irrationalité

Pierre Bel (1)

1 A2X - Théorie des Nombres et Algorithmique Arithmétique

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.

Mots clés: linear independence; irrationality; zeta; p-adic

Domaines: Théorie des nombres [math.NT]

Pierre Bel. Fonction Zêta de Hurwitz p-adique et irrationalité. 2007. ⟨hal-00145418⟩