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On a p-adic interpolation function for the Euler numbers and its derivatives. (English) Zbl 0574.12017

The authors interpolate the Euler numbers p-adically, by constructing a p-adic measure. Hence they get a corresponding analytic p-adic function \(G_ p(s,u)\), depending on one additional parameter u. The authors show, that for special values of u this function \(G_ p\) is closely connected with the p-adic L-function \(L_ p(s,\chi)\) for Dirichlet characters \(\chi\). Hence their computation of the derivative \(G'_ p(0,u)\) for \(u=\zeta_ f\) (primitive f-th root of unity) gives as a corollary results of Ferrero-Greenberg and of Diamond on \(L'_ p(0,\chi)\).
Reviewer: N.Klingen

MSC:

11S40 Zeta functions and \(L\)-functions
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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