Fonction Z\^eta de Hurwitz p-adique et irrationalit\'e
Number Theory
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.0705.1430,
title = {Fonction Z\^eta de Hurwitz p-adique et irrationalit\'e},
author = {Pierre Bel},
journal= {arXiv preprint arXiv:0705.1430},
year = {2007}
}