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math.NT2025

Existence of primitive k-normal elements for critical values over finite fields

Josimar J. R. Aguirre, Sarah F. M. Mazzini, Victor G. L. Neumann

Let $F_{q^{n}}$ be a finite field with $q^{n}$ elements. An element $I^\pm \in F_{q^{n}}$ is called $k$ -normal over $F_{q}$ if $I^\pm$ and its conjugates generate a vec…

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, AbÃlio 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…

Existence of primitive k-normal elements for critical values over finite fields

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

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