Daniela Oliveira

activity

20182022

collaborators

6 papers

math.NT2022

On the number of rational points of Artin-Schreier curves and hypersurfaces

Fabio Enrique Brochero Martínez, Daniela Alves de Oliveira

Let $F_{q^{n}}$ denote the finite field with $q^{n}$ elements. In this paper we determine the number of $F_{q^{n}}$ -rational points of the affine Artin-Schreier curve giv…

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 $Tr$ …

math.NT2020

Artin-Schreier curves given by $F_{q}$ -linearized polynomials

Daniela Oliveira, F. E. Brochero Martínez

Let $F_{q}$ be a finite field with $q$ elements, where $q$ is a power of an odd prime $p$ . In this paper we associate circulant matrices and quadratic forms with the Artin-Sc…

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.NT2018

Möbius-Frobenius maps on irreducible polynomials

F. E. Brochero Martínez, Daniela Oliveira, Lucas Reis

Let $n$ be a positive integer and let $F_{q^{n}}$ be the finite field with $q^{n}$ elements, where $q$ is a power of a prime. This paper introduces a natural action of the Proj…

math.DS2018

Invariant multi-graphs in step skew-products

Katrin Gelfert, Daniel Oliveira

We study step skew-products over a finite-state shift (base) space whose fiber maps are $C^{1}$ injective maps on the unit interval. We show that certain invariant sets have a multi-…