Representations of Definite Binary Quadratic Forms over F_q[t]

Details Representations of Definite Binary Quadratic Forms over F_q[t] Representations of Definite Binary Quadratic Forms over F_q[t]

2009-05-23

arxiv.org/abs/0905.3857v1

Illinois Journal of Mathematics, Vol. 53, No. 1 (2009); 237-250

Mathematics

Number Theory

To appear in Illinois J. Math

Scientific paper

In this paper, we prove that a binary definite quadratic form over 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 F_q[t] that
have class number one.

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