Nuno Freitas

collaborators

5 papers

math.NT2025

Revisiting the equation $x^{2} + y^{3} = z^{p}$

Nuno Freitas, Diana Mocanu, Ignasi Sanchez-Rodriguez

Let $E / Q$ be an elliptic curve and $p \geq 3$ a prime. The modular curve $X_{E}^{-} (p)$ parameterizes elliptic curves with $p$ -torsion modules anti-symplectically isomorphic to…

math.NT2025

Comparing Galois representations in the residually reducible case

Nuno Freitas, Ignasi Sánchez-Rodríguez

Let $n \geq 2$ and $p$ be a prime. Let $K$ be a number field and consider two Galois representations $ρ_1, ρ_2 : \operatorname{Gal}(\overline{K} / K) \to \operatorname{GL}_n(\mathb…

math.NT2025

On the generalized Fermat equation $x^{13} + y^{13} = z^{n}$

Alex J. Best, Sander R. Dahmen, Nuno Freitas

Let $n \in Z_{\geq 2}$ . We study the generalized Fermat equation \[x^{13}+y^{13}=z^n, \quad x,y,z \in \mathbb{Z}, \quad \gcd(x,y,z)=1.\] Using a combination of techniques,…

math.NT2025

Symplectic criteria for elliptic curves, revisited

Alain Kraus, Nuno Freitas, Ignasi Sánchez-Rodríguez

Let $ℓ$ and $p \geq 3$ be different primes. Let $E / Q_{ℓ}$ and $E^{'} / Q_{ℓ}$ be elliptic curves with isomorphic $p$ -torsion. Assume that $E$ has potentially mult…

math.NT2025

Local points on twists of $X (p)$ with applications

Nuno Freitas, Diana Mocanu

Let $E / Q$ be an elliptic curve and $p \geq 3$ a prime. The modular curve $X_{E}^{-} (p)$ parametrizes elliptic curves with $p$ -torsion modules anti-symplectically isomorphic to…

Revisiting the equation x2+y3=zp

Comparing Galois representations in the residually reducible case

On the generalized Fermat equation x13+y13=zn

Symplectic criteria for elliptic curves, revisited

Local points on twists of X(p) with applications

Revisiting the equation $x^{2} + y^{3} = z^{p}$

On the generalized Fermat equation $x^{13} + y^{13} = z^{n}$

Local points on twists of $X (p)$ with applications