#### Abstract

In this paper, the integral binary quadratic forms for which the set of represented values is closed under *k*-fold products, for even positive integers *k*, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under *k*-fold products can always be expressed by a *k*-linear mapping from (**Z**^{2})^{k} to **Z**^{2}. In the case *k* = 2, this resolves a conjecture of Aicardi and Timorin.

#### Recommended Citation

Earnest, A. G. and Fitzgerald, Robert W. "Multiplicative Properties of Integral Binary Quadratic Forms." (Jan 2008).

## Comments

To appear in

Contemporary Mathematics.