Fonction Zêta de Hurwitz p-adique et irrationalité

2007/05/10 by Pierre Bel, Bel, Pierre
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0705.1430

openalex publication_date 2007/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The knowledge on irrationality of p-adic zeta values has recently progressed. The irrationality of zeta₂(2), ζ₂(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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