Rational functions with small value set

Author(s)

Bartoli, Daniele ; Borges, Herivelto ; Quoos, Luciane

• Document type: Journal article
• Source: Journal of Algebra; v. 565, p. 16-pg., 2021-01-01.

Abstract

Let q be a prime power, and let F-q be the finite field with q elements. In connection with Galois theory and algebraic curves, this paper investigates rational functions h(x) = f (x)/g(x) is an element of F-q(x) for which the value sets V-h = {h(alpha) vertical bar alpha is an element of F-q boolean OR {infinity}} are relatively small. In particular, under certain circumstances, it proves that h(x) having a small value set is equivalent to the field extension F-q(x)/F-q(h(x)) being Galois. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 17/04681-3 - Algebraic curves over finite fields
• Grantee: Herivelto Martins Borges Filho
• Support Opportunities: Regular Research Grants