Iwasawa invariants and Kummer conguruences

Abstract

Let f( x, χ) be the Iwasawa power series for the p-adic L-function L p ( s, χ), where χ is an even nonprincipal character with conductor not divisible by p 2 (or by 8, when p = 2). The divisibility by p of the first p coefficients of f( x, χ) is characterized by Kummer type congruences of generalized Bernoulli numbers. Applications to Iwasawa invariants and class numbers of imaginary Abelian fields are discussed.