Lucas Reis

activity

20152026

most citedCounting solutions of special linear equations over finite fields

6 citations · 16 across the 25 of their papers we have counts for

collaborators

Showing 2018Show all

5 papers · 1 filter

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.RA2018

On the existence and number of invariant polynomials

Lucas Reis

This paper explores a natural action of the group $PGL_{2} (F_{q})$ on the set of monic irreducible polynomials of degree at least two over a finite field $F_{q}$ …

math.NT2018

On the factorization of iterated polynomials

Lucas Reis

Let $F_{q}$ be the finite field with $q$ elements, $f, g \in F_{q} [x]$ be polynomials of degree at least one. This paper deals with the asymptotic growth of certain arit…

math.NT2018

The dynamics of permutations on irreducible polynomials

Lucas Reis, Qiang Wang

We study degree preserving maps over the set of irreducible polynomials over a finite field. In particular, we show that every permutation of the set of irreducible polynomials of…

math.NT2018

Factorization of a class of composed polynomials

Lucas Reis

In this paper, we provide the degree distribution of irreducible factors of the composed polynomial $f (L (x))$ over $F_{q}$ , where $f (x) \in F_{q} [x]$ is irreducible and…