MINIMAL VALUE SET POLYNOMIALS OVER FIELDS OF SIZE p(3)

Autor(es)

Borges, Herivelto ^[1] ; Reis, Lucas ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Fed Minas Gerais, Dept Matemat, BR-31270901 Belo Horizonte, MG - Brazil

• Tipo de documento: Artigo de Revisão
• Fonte: Proceedings of the American Mathematical Society; v. 149, n. 9, p. 3639-3649, SEP 2021.
• Citações Web of Science: 0

Resumo

For any prime number p, and integer k >= 1, let F(p)k be the finite field of p(k) elements. A famous problem in the theory of polynomials over finite fields is the characterization of all nonconstant polynomials F epsilon F(p)k {[}x] for which the value set [F(a) : a. Fpk] has the minimum possible size left perpendicular(p(k) - 1)/ deg Fright perpendicular + 1. For k <= 2, the problem was solved in the early 1960s by Carlitz, Lewis, Mills, and Straus. This paper solves the problem for k = 3. (AU)

• Processo FAPESP: 18/03038-2 - Mapas polinomiais em corpos finitos e suas aplicações
• Beneficiário: Lucas da Silva Reis
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado