Dedekind sums with characters and class numbers of imaginary quadratic fields
Der Minkowskische Satz über die Körperdiskriminanten
Détermination des corps quartiques cycliques totalement imaginaires à groupe des classes d'idéaux d'exposant ...
Determination of all imaginary abelian sextic number fields with class number ≤ 11
Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one
Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20
Determination of the imaginary normal octic number fields with class number one which are not CM-fields
Die 2-Klassenzahlen spezieller quadratischer Zahlkörper.
Die Klassenzahl der Körper der complexen Multiplikation
Die Nullstellen der Thetareihen zu positiven binar-quadratischen Formen.
Die Theorie der Zahlstrahlen [Book]
Die Theorie der Zahlstrahlen.
Dihedral and cyclic extensions with large class numbers
This paper is a continuation of [2]. We construct unconditionally several families of number fields with large class numbers. They are number fields whose Galois closures have as the Galois groups, dihedral groups , , and cyclic groups , . We first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modification of zero density result of Kowalski-Michel, we choose subfamilies such that the corresponding -functions are zero free...
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
Discriminants of Chebyshev radical extensions
Let be any integer and fix an odd prime . Let denote the -fold composition of the Chebyshev polynomial of degree shifted by . If this polynomial is irreducible, let , where is a root of . We use a theorem of Dedekind in conjunction with previous results of the author to give conditions on that ensure is monogenic. For other values of , we apply a result of Guàrdia, Montes, and Nart to obtain a formula for the discriminant of and compute an integral basis for the ring of integers...
Discriminants of number fields defined by trinomials
Divisibility criteria for class numbers of imaginary quadratic fields
Drichlet Convolution of Contangent Numbers and Relative Class Number Formulas.