Represented value sets for integral binary quadratic forms and lattices

A characterization is given for the integral binary quadratic forms for which the set of represented values is closed under products. It is also proved that for an integral binary quadratic lattice over a Dedekind domain, the product of three values represented by the form is again a value represent...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2007-12, Vol.135 (12), p.3765-3770
Main Authors: Earnest, A. G., Fitzgerald, Robert W.
Format: Article
Language:English
Subjects:
Algebra
Combinatorics. Ordered structures
Discriminants
Equivalence relation
Exact sciences and technology
General mathematics
General, history and biography
Integers
Mathematical integrals
Mathematical lattices
Mathematics
Number theory
Order, lattices, ordered algebraic structures
Sciences and techniques of general use
Semigroups
Trigonometric identities
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A characterization is given for the integral binary quadratic forms for which the set of represented values is closed under products. It is also proved that for an integral binary quadratic lattice over a Dedekind domain, the product of three values represented by the form is again a value represented by the form. This generalizes the trigroup property observed by V. Arnold in the case of integral binary quadratic forms.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-07-08895-8