Cubic rational expressions over a finite field
| Autor: | Mattarei, Sandro, Pizzato, Marco |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 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 |
| Databáze: | arXiv |
| Externí odkaz: |
|