p-adic l-functions and sums of powers
نویسنده
چکیده
Let p be a fixed prime. Throughout this paper Zp, Qp, C and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp, cf. [1], [3], [6], [10]. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = p. Kubota and Leopoldt proved the existence of meromorphic functions, Lp(s, χ), defined over the p-adic number field, that serve as p-adic equivalents of the Dirichlet L-series, cf. [8], [10]. These p-adic L-functions interpolate the values
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