The Regulator Spectrum For Totally Real Cubic Fields.
The ring of integers of an abelian number field.
The Rosser-Iwaniec sieve in number fields, with an application
The extensions of degree 6 with minimum discriminant.
The Schur Subgroup of a Real Cyclotomic Field.
The set of minimal distances in Krull monoids
Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say . The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every...
The size function for quadratic number fields
We study the quadratic case of a conjecture made by Van der Geer and Schoof about the behaviour of certain functions which are defined over the group of Arakelov divisors of a number field. These functions correspond to the standard function for divisors of algebraic curves and we prove that they reach their maximum value for principal Arakelov divisors and nowhere else. Moreover, we consider a function , which is an analogue of exp defined on the class group, and we show it also assumes its...
The size function h° for a pure cubic field
The size of the fundamental solutions of consecutive Pell equations.
The splitting of primes in division fields of elliptic curves.
The Stickelberger element of an imaginary quadratic field
The structure of the 2-Sylow-subgroup of K2(...), I.
The structure of the tame kernels of quadratic number fields (II)
The structure of the tame kernels of quadratic number fields (I)
The Stufe of Number Fields.
The Sylow p-Subgroups of Tame Kernels in Dihedral Extensions of Number Fields
Let F/E be a Galois extension of number fields with Galois group . In this paper, we give some expressions for the order of the Sylow p-subgroups of tame kernels of F and some of its subfields containing E, where p is an odd prime. As applications, we give some results about the order of the Sylow p-subgroups when F/E is a Galois extension of number fields with Galois group .
The torsion subgroup of a family of elliptic curves over the maximal abelian extension of
We determine explicitly the structure of the torsion group over the maximal abelian extension of and over the maximal -cyclotomic extensions of for the family of rational elliptic curves given by , where is an integer.
The totally real extension of degree 6 with minimum discriminant.
The totally real extension of degree 6 with minimum discriminant.
The unit group of some fields of the form
Let and be two different prime integers such that with , and a positive odd square-free integer relatively prime to and . In this paper we investigate the unit groups of number fields .