Galois points for the Dickson-Guralnick-Zieve curve

TL;DR

This paper determines the distribution of Galois points for the Dickson-Guralnick-Zieve curve over finite fields, providing insights that modify a previously posed problem in the theory of Galois points.

Contribution

It explicitly characterizes the Galois points distribution for the Dickson-Guralnick-Zieve curve, advancing understanding in the field of algebraic curves over finite fields.

Findings

Distribution of Galois points is explicitly determined

A problem in Galois point theory is modified based on these results

Provides new insights into the structure of the Dickson-Guralnick-Zieve curve

Abstract

The Dickson-Guralnick-Zieve curve over a finite field has been studied recently by Giulietti, Korchmaros and Timpanella in several points of view. In this short note, the distribution of Galois points for this curve is determined. As a consequence, a problem posed by the present author in the theory of Galois point is modified.