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Dilogarithme \(p\)-adique, d’après R. Coleman. (French) Zbl 0554.12008

Groupe Étude Anal. Ultramétrique 10e Anneé 1982/83, No. 2, Exp. No. 17, 16 p. (1984).
The author gives an elementary approach to the results of R. F. Coleman [Invent. Math. 69, 171–208 (1982; Zbl 0516.12017)] on the existence, functional equations and other properties of \(p\)-adic multi-logarithms which are defined by the Taylor series \(\ell_ k(z)=\sum_{n\geq 1}z^ n/n^ k\). Her proofs are nice elementarization of Coleman’s original proofs.
(Of course the paper covers only part of Coleman’s article.)

MSC:

11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
30G06 Non-Archimedean function theory

Citations:

Zbl 0516.12017
Full Text: Numdam EuDML