Irrationality of Some p-adic L-values

We give a proof of the irrationality of p-adic zeta-values■(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.