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 2020Show all

6 papers · 1 filter

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 $…