Cubic rational expressions over a finite field

Sandro Mattarei; Marco Pizzato

Cubic rational expressions over a finite field

Number Theory 2023-02-21 v3 Algebraic Geometry

Authors: Sandro Mattarei , Marco Pizzato

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.

Keywords

finite fields rational maps cubic fourfolds

Cite

@article{arxiv.2104.00111,
  title  = {Cubic rational expressions over a finite field},
  author = {Sandro Mattarei and Marco Pizzato},
  journal= {arXiv preprint arXiv:2104.00111},
  year   = {2023}
}

Comments

24 pages; improved bound in Section 6 (lowered from 6q-2 to 4q), extended to include char 3; consequent rearrangement and renumbering of some theorems; discussion of related literature on cubic extensions included in Section 2

Cubic rational expressions over a finite field

Abstract

Keywords

Cite

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