Acta Mathematica Sinica, English Series

, Volume 24, Issue 4, pp 663–686 | Cite as

Irrationality of some p-adic L-values

  • Frits Beukers


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.


irrationality p-adic L-series continued fraction 

MR(2000) Subject Classification

11J72 11S40 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversitry of UtrechtUtrechtNetherlands

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