Irrationality of some p-adic L-values

We give a proof of the irrationality of p-adic zeta-values ζ _p (k) for p = 2,3 and k = 2, 3. Such results were recently obtained by 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 the irrationality of some other p-adic L-series values, and values of the p-adic Hurwitz zeta-function.