José Alves Oliveira

activity

20192022

collaborators

9 papers

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…