Representations of definite binary quadratic forms over Fq[t]

Abstract

In this paper, we prove that a binary definite quadratic form over $\mathbf{F}_q [t]$, where $q$ is odd, is completely determined up to equivalence by the polynomials it represents up to degree $3m-2$, where $m$ is the degree of its discriminant. We also characterize, when $q>13$, all the definite binary forms over $\mathbf{F}_q [t]$ that have class number one.