José Alves Oliveira

activity

20192025

collaborators

11 papers

math.NT2025

On $F_{q}$ -primitive points on hypersurfaces

José Alves Oliveira, Marcelo Oliveira Veloso

In this paper, we estimate the number of $F_{q}$ -primitive points on the affine hypersurface defined by the equation $f (x_{1}, \dots, x_{s}) = 0$ , where $f\in\mathbb{F}_q[x_1,\dots…

math.NT2022

The number of rational points of a class of superelliptic curves

José Alves Oliveira, Daniela Oliveira, F. E. Brochero Martínez

In this paper, we study the number of $F_{q^{n}}$ -rational points on the affine curve $X_{d, a, b}$ given by the equation $y^{d} = a x Tr (x) + b,$ where $Tr$ …

cs.DM2022

Dynamics of polynomial maps over finite fields

José Alves Oliveira, Fabio Enrique Brochero Martínez

Let $F_{q}$ be a finite field with $q$ elements and let $n$ be a positive integer. In this paper, we study the digraph associated to the map $x\mapsto x^n h(x^{\frac{q-1}{m}…

math.NT2021

On maximal and minimal hypersurfaces of Fermat type

José Alves Oliveira

Let $F_{q}$ be a finite field with $q = p^{n}$ elements. In this paper, we study the number of $F_{q}$ -rational points on the affine hypersurface $X$ given by $a…

math.NT2021

Diagonal equations with restricted solution sets

José Alves Oliveira

Let $F_{q}$ be a finite field with $q = p^{n}$ elements. In this paper, we study the number of solutions of equations of the form $a_{1} x_{1}^{d_{1}} + \dots + a_{s} x_{s}^{d_{s}} = b$ with $x_i…

math.NT2020

On diagonal equations over finite fields

José Alves Oliveira

Let $F_{q}$ be a finite field with $q = p^{t}$ elements. In this paper, we study the number of solutions of equations of the form $a_{1} x_{1}^{d_{1}} + \dots + a_{s} x_{s}^{d_{s}} = b$ over $\ma…

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

A note on rank-metric codes

José Alves Oliveira

Let $F_{q}$ denote the finite field with $q = p^{λ}$ elements. Maximum Rank-metric codes (MRD for short) are subsets of $M_{m \times n} (F_{q})$ whose number of elements at…

math.NT2020

Rational points on Cubic, Quartic and Sextic Curves over Finite Fields

José Alves Oliveira

Let $F_{q}$ denote the finite field with $q$ elements. In this work, we use characters to give the number of rational points on suitable curves of low degree over $\mathbb{F…

math.NT2019

Permutation Polynomials with Carlitz Rank 2

Fabio Enrique Brochero Martínez, José Alves Oliveira

Let $F_{q}$ denote the finite field with $q$ elements. The Carlitz rank of a permutation polynomial is a important measure of complexity of the polynomial. In this paper we…

math.NT2019

Permutation Binomials over Finite Fields

José Alves Oliveira, F. E. Brochero Martínez

Let $F_{q}$ denote the finite field with $q$ elements. In this paper we use the relationship between suitable polynomials and number of rational points on algebraic curves to…

On Fq​-primitive points on hypersurfaces

The number of rational points of a class of superelliptic curves

Dynamics of polynomial maps over finite fields

On maximal and minimal hypersurfaces of Fermat type

Diagonal equations with restricted solution sets

On diagonal equations over finite fields

On iterations of rational functions over perfect fields

A note on rank-metric codes

Rational points on Cubic, Quartic and Sextic Curves over Finite Fields

Permutation Polynomials with Carlitz Rank 2

Permutation Binomials over Finite Fields

On $F_{q}$ -primitive points on hypersurfaces