Fongly Zêta de Hurwitz p-adique et irrationalité
Fonction Zêta de Hurwitz p-adique et irrationalité
摘要：
关于p-adic zeta值的不合理性的认识最近有了进展。F.证明了Dirichlet级数zeta_2（2），zeta_2（3）及其它几个p-adic级数的无理性。卡利加里F. Beukers给出了一个更基本的证明这一结果。同时，T. Rivoal刚刚获得了在复杂的情况下，一些Pade逼近的Lerch功能。正是这一工作，转置到C_p，使我们能够获得非理性和线性独立的结果。
英文摘要：
The knowledge on irrationality of p-adic zeta values has recently progressed. The irrationality of zeta_2(2), ζ_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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