Fonction Zêta de Hurwitz p-adique et irrationalité

Details Fonction Zêta de Hurwitz p-adique et irrationalité Fonction Zêta de Hurwitz p-adique et irrationalité

2007-05-10

arxiv.org/abs/0705.1430v1

Mathematics

Number Theory

Scientific paper

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.

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