Irrationality of some p-adic L-values
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We give a proof of the irrationality of p-adic zeta-values ζp(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.
Keywordsirrationality p-adic L-series continued fraction
MR(2000) Subject Classification11J72 11S40
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