On the behaviour of p-adic L-functions

TextLet Lp(s,χ)Lp(s,χ) denote a Leopoldt–Kubota p-adic L  -function, where p>2p>2 and χ 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 λ-invariant associated to χ  . Assuming that λ⩽p−1λ⩽p−1, it turns out that Lp(s,χ)Lp(s,χ) behaves, in some sense, like a polynomial of degree λ. The results lead to congruences of a new type for (generalized) Bernoulli numbers.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=5aaB1d6fZDs.