Multiplicative Properties of Integral Binary Quadratic Forms

Authors

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

Comments

To appear in Contemporary Mathematics.

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 (Z²)^k to Z². 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).