Lucas Reis

activity

20172026

most citedConstruction of irreducible polynomials through rational transformations

2 citations · 3 across the 10 of their papers we have counts for

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21 papers · 1 filter

math.NT2021

Counting distinct functional graphs from linear finite dynamical systems

Lucas Reis

Let $F_{q}$ be the finite field with $q$ elements and, for each positive integer $n$ , let $A_{q} (n)$ be the number of non isomorphic functional graphs arising from $\mathbb F_q…

math.NT2021

The additive index of polynomials over finite fields

Lucas Reis, Qiang Wang

In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms…

math.NT2021

Permutation polynomials from a linearized decomposition

Lucas Reis, Qiang Wang

In this paper we discuss the permutational property of polynomials of the form $f (L (x)) + k (L (x)) \cdot M (x) \in F_{q^{n}} [x]$ over the finite field $F_{q^{n}}$ , where $L,…

math.NT2021

On primitive elements of finite fields avoiding affine hyperplanes

Arthur Fernandes, Lucas Reis

Let $n \geq 2$ be an integer and let $F_{q}$ be the finite field with $q$ elements, where $q$ is a prime power. Given $F_{q}$ -affine hyperplanes $\mathcal A_1, \ldots, \m…

math.NT2020

On iterations of rational functions over perfect fields

José Alves Oliveira, Daniela Oliveira, Lucas Reis

Let $K$ be a perfect field of characterstic $p \geq 0$ and let $R \in K (x)$ be a rational function. This paper studies the number $Δ_{α, R} (n)$ of distinct solutions o…

math.NT2020

Character sums over affine spaces and applications

Lucas Reis

Given a finite field $F_{q}$ , a positive integer $n$ and an $F_{q}$ -affine space $A \subseteq F_{q^{n}}$ , we provide a new bound on the sum $\sum_{a\in \m…