Represented Value Sets for Integral Binary Quadratic Forms and Lattices

Authors

A. G. Earnest, Southern Illinois University CarbondaleFollow
Robert W. Fitzgerald, Southern Illinois University CarbondaleFollow

Comments

First published in Proceedings of the American Mathematical Society, 135, 3765-3770, published by the American Mathematical Society. © Copyright 2007 American Mathematical Society

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 the ring of integers of a global field, the product of three values represented by the form is again a value represented by the form. This generalizes the trigroup property discovered by V. Arnold for the case of integral binary quadratic forms.

Recommended Citation

Earnest, A. G. and Fitzgerald, Robert W. "Represented Value Sets for Integral Binary Quadratic Forms and Lattices." (Jan 2007).