A differential criterion for complete intersections.
A generalization of the Chowla-Selberg formula.
Applications of spinor class fields: embeddings of orders and quaternionic lattices
We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.
Approximatting rings of integers in number fields
In this paper we study the algorithmic problem of finding the ring of integers of a given algebraic number field. In practice, this problem is often considered to be well-solved, but theoretical results indicate that it is intractable for number fields that are defined by equations with very large coefficients. Such fields occur in the number field sieve algorithm for factoring integers. Applying a variant of a standard algorithm for finding rings of integers, one finds a subring of the number field...
Average values of L-series in function fields.
Bestimmung der Idealklassenzahl in gewissen normalen einfachen Algebren.
Binary forms and orders of algebraic number fields (Erratum).
Cale Bases in Algebraic Orders
Let be a non-maximal order in a finite algebraic number field with integral closure . Although is not a unique factorization domain, we obtain a positive integer and a family (called a Cale basis) of primary irreducible elements of such that has a unique factorization into elements of for each coprime with the conductor of . Moreover, this property holds for each nonzero when the natural map is bijective. This last condition is actually equivalent to several properties linked...
Definite quaternion orders of class number one
Embedding orders into central simple algebras
The question of embedding fields into central simple algebras over a number field was the realm of class field theory. The subject of embedding orders contained in the ring of integers of maximal subfields of such an algebra into orders in that algebra is more nuanced. The first such result along those lines is an elegant result of Chevalley [6] which says that with the ratio of the number of isomorphism classes of maximal orders in into which the ring of integers of can be embedded...
Functional equations for zeta functions of non-Gorenstein orders in global fields.
Fundamental units for orders of unit rank 1 and generated by a unit
Let ε be an algebraic unit for which the rank of the group of units of the order ℤ[ε] is equal to 1. Assume that ε is not a complex root of unity. It is natural to wonder whether ε is a fundamental unit of this order. It turns out that the answer is in general yes, and that a fundamental unit of this order can be explicitly given (as an explicit polynomial in ε) in the rare cases when the answer is no. This paper is a self-contained exposition of the solution to this problem, solution which was...
Generalization of a theorem of Siegel
Height preserving linear transformations on semisimple K-algebras.
Kummer type system of congruences and bases of Stickelberger subideals
Les fonctions des algèbres simples, I
Les fonctions des algèbres simples, II
Modules over regular algebras of dimension 3.
On the imbeddings of imaginary quadratic orders in definite quaternion orders.
Orders of a quaternion algebra over a number field.