Dedekind sums and power residue symbols
Dedekind sums with characters and class numbers of imaginary quadratic fields
Densities of 4-ranks of K₂(𝒪)
Density results for the 2-classgroups of imaginary quadratic fields.
Der Satz von Erdös und Fuchs in reell-quadratischen Zahlkörpern
Dernier théorème de Fermat et groupes de classes dans certains corps quadratiques imaginaires
Détermination explicite des courbes elliptiques ayant un groupe de torsion non trivial sur des corps de nombres quadratiques sur Q.
Développement en fraction continue à l'entier le plus proche, idéaux α-réduits et un problème d'Eisenstein
Développement en fraction continue à l'entier supérieur, idéaux 0-réduits et un problème d'Eisenstein
Die 2-Klassenzahlen spezieller quadratischer Zahlkörper.
Die Klassengruppen quadratischer und kubischer Zahlkörper und die Selmer-Gruppen gewisser elliptischer Kurven.
Die Maße der Geschlechter quadratischer Formen vom Range ...3 in quadratischen Zahlkörpern.
Die Nullstellen der Thetareihen zu positiven binar-quadratischen Formen.
Die Stufe von Ordnungen ganzer Zahlen in algebraischen Zahlkörpern.
Different groups of circular units of a compositum of real quadratic fields
There are many different definitions of the group of circular units of a real abelian field. The aim of this paper is to study their relations in the special case of a compositum k of real quadratic fields such that -1 is not a square in the genus field K of k in the narrow sense. The reason why fields of this type are considered is as follows. In such a field it is possible to define a group C of units (slightly bigger than Sinnott's group of circular units) such that the Galois...
Digital expansions in real algebraic quadratic fields.
Diophantine equations and class number of imaginary quadratic fields
Let A, D, K, k ∈ ℕ with D square free and 2 ∤ k,B = 1,2 or 4 and , and let denote the class number of the imaginary quadratic field . In this paper, we give the all-positive integer solutions of the Diophantine equation Ax² + μ₁B = K((Ay² + μ₂B)/K)ⁿ, 2 ∤ n, n > 1 and we prove that if D > 1, then , where D, and n satisfy , x ∈ ℕ, 2 ∤ n, n > 1. The results are valuable for the realization of quadratic field cryptosystem.
Diophantine equations and class numbers of real quadratic fields
Diophantine quadruples in .
Diskriminanten und Picard-Invarianten freier quadratischer Erweiterungen.