Leopoldt's conjecture for imaginary Galois number fields

Abstract

In studying Leopoldt's conjecture for Galois number fields a sufficient condition is proposed which includes the known criteria and moreover refers only to the character table of the Galois group in question. Hence it may easily be checked. Tables of the computations are given. New examples, if only few, of imaginary number fields are exhibited for which Leopoldt's conjecture is proved to be true for all primes p . Some of them are covered by some kind of “Verschiebungssatz” for Leopoldt's conjecture.