A Note on Siegel's Lemma Over Number Fields.
A note on Sinnott's index formula
Let k be an (imaginary or real) abelian number field whose conductor has two distinct prime divisors. We shall construct a basis for the group C of circular units in k and compute the index of C in the group E of units in k. This result is a generalization of Theorem 3.3 in a previous paper [1].
A note on the existence of certain infinite families of imaginary quadratic fields
A note on the ideal class group of the cyclotomic ℤₚ-extension of a totally real number field
A pure arithmetical characterization for certain fields with a given class group
A question on the discriminants of involutions of central division algebras.
A Stark conjecture “over ” for abelian -functions with multiple zeros
Suppose is an abelian extension of number fields. Stark’s conjecture predicts, under suitable hypotheses, the existence of a global unit of such that the special values for all characters of can be expressed as simple linear combinations of the logarithms of the different absolute values of .In this paper we formulate an extension of this conjecture, to attempt to understand the values when the order of vanishing may be greater than one. This conjecture no longer predicts the existence...
A type of class group for imaginary quadratic fields
Abschätzungen für die Klassenzahlen der quadratischen Körper
Acknowledgment of priority
Addendum: Les extensions quadratiques du corps des raionnels, ou du corps de Gauss, ou du coprs des racines cubiques de l'unité de calibres 1.
Additive Galois module structure and Chinburg's invariant.
Algebraic integers of small discriminant
Amélioration d'une congruence pour certains éléments de Stickelberger quadratiques
An application of the p-adic class number formula.
An inequality for the class number.
An infinite family of pairs of quadratic fields ℚ(√D) and ℚ(√mD) whose class numbers are both divisible by 3
Annihilators for the class group of a cyclic field of prime power degree
Annihilators of minus class groups of imaginary abelian fields
For certain imaginary abelian fields we find annihilators of the minus part of the class group outside the Stickelberger ideal. Depending on the exact situation, we use different techniques to do this. Our theoretical results are complemented by numerical calculations concerning borderline cases.
Annihilators of the class group of a compositum of quadratic fields
This paper is devoted to a construction of new annihilators of the ideal class group of a tamely ramified compositum of quadratic fields. These annihilators are produced by a modified Rubin’s machinery. The aim of this modification is to give a stronger annihilation statement for this specific type of fields.