Lucas Reis

collaborators

3 papers

math.NT2017

A note on primitive $1 -$ normal elements over finite fields

Lucas Reis

Let $q$ be a prime power of a prime $p$ , $n$ a positive integer and $F_{q^{n}}$ the finite field with $q^{n}$ elements. The $k -$ normal elements over finite fields were introduc…

math.NT2016

On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

Fabio E. Brochero Martínez, Theodoulos Garefalakis, Lucas Reis +1

In this paper, we find a lower bound for the order of the group $⟨ θ + α ⟩ \subset F_{q}^{*}$ , where $α \in F_{q}$ , $θ$ is a generic root of the po…

math.NT2016

The action of $GL_{2} (F_{q})$ on irreducible polynomials over $\F_q$

Lucas Reis

Let $\F_q$ be the finite field with $q$ elements, $p=\Char \F_q$. The group $\GL_2(\F_q)$ acts naturally in the set of irreducible polynomials over $\F_q$ of degree at least $2$ . I…

A note on primitive 1−normal elements over finite fields

On the multiplicative order of the roots of bXqr+1−aXqr+dX−c

The action of GL2​(Fq​) on irreducible polynomials over $\F_q$

A note on primitive $1 -$ normal elements over finite fields

On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

The action of $GL_{2} (F_{q})$ on irreducible polynomials over $\F_q$