Abílio Lemos

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math.NT2024

On the functional graph of $f (X) = X (X^{q - 1} - c)^{q + 1},$ over quadratic extensions of finite fields

Josimar J. R. Aguirre, Abílio Lemos, Victor G. L. Neumann

Let $F_{q}$ be the finite field with $q$ elements. In this paper we will describe the dynamics of the map $f (X) = X (X^{q - 1} - c)^{q + 1},$ with $c \in F_{q}^{*},$ over…

math.NT2022

Quadratic Symmetric Polynomials and an analogue of the Davenport Constant

Hemar Godinho, Abílio Lemos, Victor Neumann +1

In this paper, we define the constant $D (φ, p)$ , an analogue for the Davenport constant, for sequences on the finite field $F_{p}$ , defined via quadratic symmetric polynomia…

math.NT2022

On arithmetic progressions in finite fields

Abílio Lemos, Victor Neumann, Sávio Ribas

In this paper, we explore the existence of $m$ -terms arithmetic progressions in $F_{q^{n}}$ with a given common difference whose terms are all primitive elements, and at lea…

On the functional graph of f(X)=X(Xq−1−c)q+1, over quadratic extensions of finite fields

Quadratic Symmetric Polynomials and an analogue of the Davenport Constant

On arithmetic progressions in finite fields

On the functional graph of $f (X) = X (X^{q - 1} - c)^{q + 1},$ over quadratic extensions of finite fields