On the behaviour of p-adic L-functions

Text. Let L-p(s, chi) denote a Leopoldt-Kubota p-adic L-function, where p > 2 and chi is a nonprincipal even character of the first kind. The aim of this article is to study how the values assumed by this function depend on the Iwasawa lambda-invariant associated to chi. Assuming that lambda <= p - 1, it turns out that L-p(s, chi) behaves, in some sense, like a polynomial of degree chi. The results lead to congruences of a new type for (generalized) Bernoulli numbers. Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=5aaB1d6fZDs. (C) 2009 Elsevier Inc. All rights reserved.