Die Ungleichung von Castelnuovo.
Die Verteilung der Primteiler von Polynomen auf Restklassen. I.
Die Verteilung der Primteiler von Polynomen auf Restklassen. II.
Die Weilsche "Explizite Formel" und temperierte Distributionen.
Die Zerlegungscharaktere abelscher total reeller Erweiterungen reeller Funktionenkörper einer Variablen.
Diedergruppe und Reziprozitätsgesetz.
Differences in sets of lengths of Krull monoids with finite class group
Let be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary -groups have the same system of sets of lengths if and only if they are isomorphic.
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...
Digit derivatives and application to zeta measures
Digital expansions in real algebraic quadratic fields.
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...
Dihedral extensions of Q of degree 21 which contain non-Galois extensions with class number not divisible by l
Dilogarithms, Regulators and p-adic L-functions.
Dimensions of spaces of cusp forms over function 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 equations and identities.
Diophantine equations in cyclotomic fields.
Diophantine equations over global function fields. II: -integral solutions of Thue equations.
Diophantine quadruples in .