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

40 papers

math.CO2026

On a class of combinatorial group invariants

Arthur Fernandes, Claudio Qureshi, Lucas Reis +1

In this paper, we explore group invariants arising from combinatorial structures associated with finite groups, including the functional graphs of power maps and the well-studied p…

math.RA2026

Polynomial identities, central polynomials and cocharacters of $M_{2} (F)$ with $G$ -graded involution

Rafael Bezerra dos Santos, Lucas Reis

Let $F$ be a field of characteristic zero, $G$ be a finite abelian group and $M_{2} (F)$ be the algebra of $2 \times 2$ matrices over $F$ . In this paper, we consider all $G$ -graded inv…

math.RA2026

Polynomial identities, central polynomials and cocharacters of $M_{2} (F)$ with transpose superinvolution

Rafael Bezerra dos Santos, Lucas Reis

Let $F$ be a field of characteristic zero and consider $M_{2} (F),$ the algebra of $2 \times 2$ matrices over $F,$ with canonical $Z_{2}$ -grading and endowed with transpose supe…

math.CO2026

Graphs from quadratic forms and vector spaces over finite fields

Jean Godard, Lucas Reis

Let $q$ be an odd prime power, let $n \geq 2$ , and let $V ⊊ F_{q^{n}}$ be a proper $F_{q}$ -vector subspace. Given a nonzero quadratic form $Q(X,Y)\in \mathbb F_{q…

math.NT2022

The average density of K-normal elements over finite fields

Lucas Reis

Let $q$ be a prime power and, for each positive integer $n \geq 1$ , let $F_{q^{n}}$ be the finite field with $q^{n}$ elements. Motivated by the well known concept of normal eleme…

math.CO2022

Paley-like graphs over finite fields from vector spaces

Lucas Reis

Motivated by the well-known Paley graphs over finite fields and their generalizations, in this paper we explore a natural multiplicative-additive analogue of such graphs arising fr…

math.NT2021

The existence of $F_{q}$ -primitive points on curves using freeness

Stephen D. Cohen, Giorgos Kapetanakis, Lucas Reis

Let $C_{Q}$ be the cyclic group of order $Q$ , $n$ a divisor of $Q$ and $r$ a divisor of $Q / n$ . We introduce the set of $(r, n)$ -free elements of $C_{Q}$ and derive a l…

cs.DM2021

On the functional graph of the power map over finite groups

Claudio Qureshi, Lucas Reis

In this paper we study the description of the functional graphs associated with the power maps over finite groups. We present a structural result which describes the isomorphism cl…

math.NT2021

Counting distinct functional graphs from linear finite dynamical systems

Lucas Reis

Let $F_{q}$ be the finite field with $q$ elements and, for each positive integer $n$ , let $A_{q} (n)$ be the number of non isomorphic functional graphs arising from $\mathbb F_q…

math.NT2021

The additive index of polynomials over finite fields

Lucas Reis, Qiang Wang

In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms…

math.NT2021★ 1 cited

Permutation polynomials from a linearized decomposition

Lucas Reis, Qiang Wang

In this paper we discuss the permutational property of polynomials of the form $f (L (x)) + k (L (x)) \cdot M (x) \in F_{q^{n}} [x]$ over the finite field $F_{q^{n}}$ , where $L,…

math.NT2021

On primitive elements of finite fields avoiding affine hyperplanes

Arthur Fernandes, Lucas Reis

Let $n \geq 2$ be an integer and let $F_{q}$ be the finite field with $q$ elements, where $q$ is a prime power. Given $F_{q}$ -affine hyperplanes $\mathcal A_1, \ldots, \m…

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

Character sums over affine spaces and applications

Lucas Reis

Given a finite field $F_{q}$ , a positive integer $n$ and an $F_{q}$ -affine space $A \subseteq F_{q^{n}}$ , we provide a new bound on the sum $\sum_{a\in \m…

math.NT2020

Arithmetic constraints of polynomial maps through discrete logarithms

Lucas Reis

Let $q$ be a prime power, let $F_{q}$ be the finite field with $q$ elements and let $θ$ be a generator of the cyclic group $F_{q}^{*}$ . For each $a \in F_{q}^{*}$ , let…

math.NT2020★ 4 cited

Generators of finite fields with prescribed traces

Lucas Reis, Sávio Ribas

This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result…

math.NT2020

A note on additive characters of finite fields

Lucas Reis

Let $F_{q}$ be the finite field with $q$ elements, where $q$ is a prime power and, for each integer $n \geq 1$ , let $F_{q^{n}}$ be the unique $n$ -degree extension of $\ma…

math.NT2020★ 6 cited

Counting solutions of special linear equations over finite fields

Lucas Reis

Let $q$ be a prime power, let $F_{q}$ be the finite field with $q$ elements and let $d_{1}, \dots, d_{k}$ be positive integers. In this note we explore the number of solutions $…

math.NT2019

Mean value theorems for a class of density-like arithmetic functions

Lucas Reis

This paper provides a mean value theorem for arithmetic functions $f$ defined by $f (n) = d ∣ n \prod g (d),$ where $g$ is an arithmetic function taking values in $(0, 1]$ and satisfy…

math.NT2019★ 2 cited

Construction of irreducible polynomials through rational transformations

Daniel Panario, Lucas Reis, Qiang Wang

Let $F_{q}$ be the finite field with $q$ elements, where $q$ is a power of a prime. We discuss recursive methods for constructing irreducible polynomials over $F_{q}$ o…

math.NT2019

Permutations from an arithmetic setting

Lucas Reis, Sávio Ribas

Let $m, n$ be positive integers such that $m > 1$ divides $n$ . In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1, n]:=\{1, \ldots, n\…

math.NT2019★ 1 cited

Factorization of composed polynomials and applications

F. E. Brochero Martínez, Lucas Reis, Lays Silva

Let $F_{q}$ be the finite field with $q$ elements, where $q$ is a prime power and $n$ be a positive integer. In this paper, we explore the factorization of $f (x^{n})$ over $…

math.NT2019

Dynamics of the $a$ -map over residually finite Dedekind Domains and applications

Claudio Qureshi, Lucas Reis

Let $D$ be a residually finite Dedekind domain, $a \in D$ be a nonzero element and $n$ be a nonzero ideal of $D$ . In this paper we describe t…

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…

On a class of combinatorial group invariants

Polynomial identities, central polynomials and cocharacters of M2​(F) with G-graded involution

Polynomial identities, central polynomials and cocharacters of M2​(F) with transpose superinvolution

Graphs from quadratic forms and vector spaces over finite fields

The average density of K-normal elements over finite fields

Paley-like graphs over finite fields from vector spaces

The existence of Fq​-primitive points on curves using freeness

On the functional graph of the power map over finite groups

Counting distinct functional graphs from linear finite dynamical systems

The additive index of polynomials over finite fields

Permutation polynomials from a linearized decomposition

On primitive elements of finite fields avoiding affine hyperplanes

On iterations of rational functions over perfect fields

Character sums over affine spaces and applications

Arithmetic constraints of polynomial maps through discrete logarithms

Generators of finite fields with prescribed traces

A note on additive characters of finite fields

Counting solutions of special linear equations over finite fields

Mean value theorems for a class of density-like arithmetic functions

Construction of irreducible polynomials through rational transformations

Permutations from an arithmetic setting

Factorization of composed polynomials and applications

Dynamics of the a-map over residually finite Dedekind Domains and applications

Möbius-Frobenius maps on irreducible polynomials

Polynomial identities, central polynomials and cocharacters of $M_{2} (F)$ with $G$ -graded involution

Polynomial identities, central polynomials and cocharacters of $M_{2} (F)$ with transpose superinvolution

The existence of $F_{q}$ -primitive points on curves using freeness

Dynamics of the $a$ -map over residually finite Dedekind Domains and applications