Illinois Journal of Mathematics

Representations of definite binary quadratic forms over Fq[t]

Jean Bureau and Jorge Morales

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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.

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Illinois J. Math., Volume 53, Number 1 (2009), 237-249.

First available in Project Euclid: 22 January 2010

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Primary: 11E25: Sums of squares and representations by other particular quadratic forms 11E12: Quadratic forms over global rings and fields 11E41: Class numbers of quadratic and Hermitian forms 11D09: Quadratic and bilinear equations


Bureau, Jean; Morales, Jorge. Representations of definite binary quadratic forms over F q [ t ]. Illinois J. Math. 53 (2009), no. 1, 237--249. doi:10.1215/ijm/1264170848.

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