We study and partially classify cubic rational expressions over a finite field F_q, up to equivalence given by composition with independent M¨obius transformations on each side. When q is even we obtain a full classification. When q is odd we restrict our classification to expressions with at most three ramification points. However, we prove a general upper bound of 4q for the total number of equivalence classes.
Mattarei, S., Pizzato, M. (2024). Cubic rational expressions over a finite field. JOURNAL OF ALGEBRA AND ITS APPLICATIONS [10.1142/S0219498825503190].
Cubic rational expressions over a finite field
Mattarei S.
;
2024
Abstract
We study and partially classify cubic rational expressions over a finite field F_q, up to equivalence given by composition with independent M¨obius transformations on each side. When q is even we obtain a full classification. When q is odd we restrict our classification to expressions with at most three ramification points. However, we prove a general upper bound of 4q for the total number of equivalence classes.
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