Shiratani, Katsumi; Yamamoto, Sunao On a p-adic interpolation function for the Euler numbers and its derivatives. (English) Zbl 0574.12017 Mem. Fac. Sci., Kyushu Univ., Ser. A 39, 113-125 (1985). 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 Cited in 4 ReviewsCited in 45 Documents MSC: 11S40 Zeta functions and \(L\)-functions 11B39 Fibonacci and Lucas numbers and polynomials and generalizations Keywords:Euler numbers; p-adic measure; p-adic L-function PDFBibTeX XMLCite \textit{K. Shiratani} and \textit{S. Yamamoto}, Mem. Fac. Sci., Kyushu Univ., Ser. A 39, 113--125 (1985; Zbl 0574.12017) Full Text: DOI