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arXiv · 2104.00111

Cubic rational expressions over a finite field

Sandro Mattarei·Marco Pizzato
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Abstract

We study and partially classify cubic rational expressions $g(x)/h(x)$ over a finite field $\mathbb{F}_q$, up to pre- and post-composition with independent M\"obius transformations. In particular, we obtain a full classification when $q$ is even, and prove an upper bound of $4q$ for the number of equivalence classes when $q$ is odd.

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Sandro Mattarei, Marco Pizzato. 2021-03-31. Cubic rational expressions over a finite field. https://arxiv.org/abs/2104.00111

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