Lucas Reis

collaborators

4 papers

math.NT2025

Minimal Value Set Polynomials

Herivelto Borges, Lucas Reis

A well-known problem in the theory of polynomials over finite fields is the characterization of minimal value set polynomials (MVSPs) over the finite field $F_{q}$ , where $q…

math.NT2025

Normal points on Artin-Schreier curves over finite fields

Giorgos Kapetanakis, Lucas Reis

In 2022, S.D. Cohen and the two authors introduced and studied the concept of $(r, n)$ -freeness on finite cyclic groups $G$ for suitable integers $r, n$ , which is an arithmetic way…

math.NT2025

Iterating additive polynomials over finite fields

Lucas Reis

Let $q$ be a power of a prime $p$ , let $F_{q}$ be the finite field with $q$ elements and, for each nonconstant polynomial $F \in F_{q} [X]$ and each integer $n \geq 1$ , l…

math.NT2024

Existence of normal elements with prescribed norms

Arthur Fernandes, Daniel Panario, Lucas Reis

For each positive integer $n$ , let $F_{q^{n}}$ be the unique $n$ -degree extension of the finite field $F_{q}$ with $q$ elements, where $q$ is a prime power. It is known…