Galois groups of exponent two and the Brumer-Stark conjecture.
Galois module structure of the rings of integers in wildly ramified extensions
The main results of this paper may be loosely stated as follows.Theorem.— Let and be sums of Galois algebras with group over algebraic number fields. Suppose that and have the same dimension and that they are identical at their wildly ramified primes. Then (writing for the maximal order in )In many cases The role played by the root numbers of and at the symplectic characters of in determining the relationship between the -modules and is described. The theorem includes...
Généralisation d'un théorème de I. M. Vinogradov à un corps de séries formelles sur un corps fini
Generalised Mertens and Brauer-Siegel theorems
Gross’ conjecture for extensions ramified over four points of
In this paper, under a mild hypothesis, we prove a conjecture of Gross for the Stickelberger element of the maximal abelian extension over the rational function field unramified outside a set of four degree-one places.
Hecke eigenvalues for real quadratic fields.
Heckesche Systeme idealer Zahlen und Knesersche Körpererweiterungen
Einleitung. Eine klassische Konstruktion aus der algebraischen Zahlentheorie ist folgende: Zu jedem algebraischen Zahlkörper K kann man ein sogenanntes System idealer Zahlen S zuordnen, welches eine Untergruppe der multiplikativen Gruppe ℂ* der komplexen Zahlen ist derart, daß die Faktorgruppe S/K* in kanonischer Weise isomorph zu der Klassengruppe von K ist. Diese Konstruktion geht auf Hecke [5] zurück und hat folgende wichtige Eigenschaft, die auch bei dem Hilbertschen Klassenkörper zu K vorkommt:...
Higher regulators and Hecke L-series of imaginary quadratic fields I.
Homologie du groupe linéaire et polylogarithmes
Horizontal Factorizations of Certain Hasse-Weil Zeta Functions - a Remark on a Paper by Taniyama
Hyperbolic manifolds and special values of Dedekind zeta-functions.
Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung.
Invariant differentials and -functions. Reciprocity law for quadratic fields and elliptic curves over
Iwasawa L-Functions of Varieties over Algebraic Number Fields.
Jacobi-sum Hecke characters and Gauss-sum identities
Jacobi-sum Hecke characters of imaginary quadratic fields
Kronecker’s solution of Pell’s equation for CM fields
We generalize Kronecker’s solution of Pell’s equation to CM fields whose Galois group over is an elementary abelian 2-group. This is an identity which relates CM values of a certain Hilbert modular function to products of logarithms of fundamental units. When is imaginary quadratic, these CM values are algebraic numbers related to elliptic units in the Hilbert class field of . Assuming Schanuel’s conjecture, we show that when has degree greater than 2 over these CM values are transcendental....
La résolution des conjectures d'Artin dans les cas ... et ... par les méthodes de Langlands
l-adic L-functions and rational function measures
Laurent coefficients of the zeta function of an indefinite quadratic form