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Irrationality of some p-adic L-values

F. Beukers
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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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F. Beukers. 2006-06-20. Irrationality of some p-adic L-values. https://arxiv.org/abs/math/0603277

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