F. E. B. Mart'inez

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20192025

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6 papers · 1 filter

math.NT2025

The dynamics of a function family over quadratic extensions of finite fields

Fabio E. Brochero Martínez, Hugo R. Teixeira

Let $F_{q}$ be the finite field with $q = p^{s}$ elements, where $p$ is an odd prime and $s$ a positive integer. In this paper, we define the function $f(X)=(cX^q+aX)(X^{q}-X)^{…

math.NT2023

Counting roots of fully triangular polynomials over finite fields

José Gustavo Coelho, Fabio Enrique Brochero Martínez

Let $F_{q}$ be a finite field with $q$ elements, $f \in F_{q} [x_{1}, \dots, x_{n}]$ a polynomial in $n$ variables and let us denote by $N (f)$ the number of roots of $f$ i…

math.NT2022

On the direct and inverse zero-sum problems over $C_{n} ⋊_{s} C_{2}$

Danilo Vilela Avelar, Fabio Enrique Brochero Martínez, Sávio Ribas

Let $C_{n}$ be the cyclic group of order $n$ . In this paper, we provide the exact values of some zero-sum constants over $C_{n} ⋊_{s} C_{2}$ where $s \neq \equiv \pm 1 (mod n)$ , namely…

math.NT2021

The main zero-sum constants over $D_{2 n} \times C_{2}$

Fabio Enrique Brochero Martínez, Abílio Lemos, B. K. Moriya +1

Let $C_{2}$ be the cyclic group of order $2$ and $D_{2 n}$ be the dihedral group of order $2 n$ , where $n$ is even. In this paper, we provide the exact values of some zero-sum constant…

math.NT2021

Extremal product-one free sequences over $C_{n} ⋊_{s} C_{2}$

Fabio Enrique Brochero Martínez, Sávio Ribas

Let $G$ be a finite group multiplicatively written. The small Davenport constant of $G$ is the maximum positive integer $d (G)$ such that there exists a sequence $S$ of length…

math.NT2019

The estimation of the number of Irreducible Binomials

Fabio Enrique Brochero Martínez, Lays Grazielle Cardoso Silva de Jesus

Let $F_{q}$ be the finite field with $q$ elements, and $T$ a positive integer. In this article we find a sharp estimative of the total number of monic irreducible binomials…