João Paulo Guardieiro

collaborators

6 papers

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.AG2026

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q + 1} = X^{n} (X^{n} + 1)$

João Paulo Guardieiro, Yuri da Silva, Saeed Tafazolian

We study the algebraic curve over $F_{q^{2}}$ defined by $y^{q + 1} = x^{n} (x^{n} + 1)$ , where $n$ is a positive integer coprime to the characteristic. We first prove (when $q$ is o…

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.AG2025

The ranks of twists of an elliptic curve in characteristic $3$

João Paulo Guardieiro

Starting from the elliptic curve $E : y^{2} = x^{3} - x$ over $F_{9}$ , a curve $X$ over $F_{3^{2 n}}$ and a cyclic cover of $X$ of degree $m \in \{2,3…

math.AG2024

Tate-Shafarevich results for quartic twists in characteristic $2$

Herivelto Borges, João Paulo Guardieiro, Cecília Salgado +1

The aim of this paper is to present elliptic curves defined over function fields of even characteristic having arbitrarily large Mordell-Weil rank. More precisely, we study ellipti…

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​

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve Yq+1=Xn(Xn+1)