Number of equivalence classes of rational functions over finite fields

被引：0

作者：

Hou, XIANG-DoNG ^{[1
]}

机构：

[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

来源：

ACTA ARITHMETICA | 2025年 / 218卷 / 02期

关键词：

finite field; general linear group; projective linear group; rational; function; DECOMPOSITION; POLYNOMIALS;

D O I：

10.4064/aa240317-14-12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two rational functions f, g is an element of F-q(X) are said to be equivalent if there exist phi, psi is an element of F-q(X) of degree 1 such that g = phi degrees f degrees psi. We give an explicit formula for the number of equivalence classes of rational functions of a given degree in F-q(X). This result should provide guidance for the current and future work on classifications of low degree rational functions over finite fields. We also determine the number of equivalence classes of polynomials of a given degree in F-q[X].

引用

页码：97 / 136

页数：40

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