João Paulo Guardieiro

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20202026

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math.NT2026

On planar functions over $F_{q^{3}}$

João Paulo Guardieiro, Adler Marques, Luciane Quoos +1

Let $F_{q}$ denote the finite field of order $q$ . For $q$ odd, we investigate the planarity over $F_{q^{3}}$ of the family $$ f_{E,A,B,C,D}(X) := EX^2+ AX^{q+1}+ BX^{…

math.NT2025

Minimal value set binomials and Frobenius nonclassical curves

Tiago Aprigio, João Paulo Guardieiro

In this paper, we characterize all minimal value set binomials over $F_{q}$ , that is, binomials whose size of the set of images is the smallest possible. With this informati…

math.NT2020

On the existence of pairs of primitive and normal elements over finite fields

Cícero Carvalho, João Paulo Guardieiro, Victor G. L. Neumann +1

Let $F_{q^{n}}$ be a finite field with $q^{n}$ elements, and let $m_{1}$ and $m_{2}$ be positive integers. Given polynomials $f_{1} (x), f_{2} (x) \in F_{q} [x]$ with $\textrm{deg…

On planar functions over Fq3​

Minimal value set binomials and Frobenius nonclassical curves

On the existence of pairs of primitive and normal elements over finite fields

On planar functions over $F_{q^{3}}$