Irrationality of some p-adic L-values

2006/03/12 by Beukers, F.
#11J72 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0603277

Abstract

We give a proof of the irrationality of the p-adic zeta-values ζ_p(k) for p=2,3 and k=2,3. Such results were recently obtained by F.Calegari as an application of overconvergent p-adic modular forms. In this paper we present an approach using classical continued fractions discovered by Stieltjes. In addition we show irrationality of some other p-adic L-series values, and values of the p-adic Hurwitz zeta-function.

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