Represented value sets for integral binary quadratic forms and lattices

Author:

Earnest A.,Fitzgerald Robert

Abstract

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. [1] F. Aicardi and V. Timorin, On binary quadratic forms with semigroup property, preprint.

2. Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world;Arnold, V.;Bull. Braz. Math. Soc. (N.S.),2003

3. A Wiley-Interscience Publication;Cox, David A.,1989

4. Class groups in the genus and spinor genus of binary quadratic lattices;Earnest, A. G.;Proc. London Math. Soc. (3),1980

5. [5] O. T. O’Meara, Introduction to Quadratic Forms, Springer-Verlag, Berlin, 1963.

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