Nuno Freitas

activity

20112026

most citedThe Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields

41 citations · 104 across the 25 of their papers we have counts for

collaborators

31 papers

math.NT2026

On Fermat-type equations of signature $(r, r, p)$

Nuno Freitas

Let $r \geq 11$ be a prime. We show that there are infinitely many integers $C$ for which the Fermat-type equation $x^{r} + y^{r} = C z^{p}$ has no non-trivial primitive solutions for all s…

math.NT2026

Congruences and ramified primes in fields of coefficients of newforms

Nuno Freitas, Filip Gawron

We investigate the splitting behavior of $ℓ$ in the coefficient field of a newform $f$ of level $N$ , under the assumption that $f$ is congruent modulo a prime above $ℓ$ to an…

math.NT2023

On Darmon's program for the Generalized Fermat equation, II

Nicolas Billerey, Imin Chen, Luis Dielefait +1

We obtain additional Diophantine applications of the methods surrounding Darmon's program for the generalized Fermat equation developed in the first part of this series of papers.…

math.NT2022

Two results on $x^{r} + y^{r} = d z^{p}$

Nuno Freitas, Filip Najman

This note proves two theorems regarding Fermat-type equation $x^{r} + y^{r} = d z^{p}$ where $r \geq 5$ is a prime. Our main result shows that, for infinitely many integers~ $d$ , the previ…

math.NT2022

On Darmon's program for the generalized Fermat equation, I

Nicolas Billerey, Imin Chen, Luis Dieulefait +1

In 2000, Darmon described a program to study the generalized Fermat equation using modularity of abelian varieties of $GL_{2}$ -type over totally real fields. The original ap…

math.NT2022

On Galois inertial types of elliptic curves over $Q_{ℓ}$

Lassina Dembélé, Nuno Freitas, John Voight

We provide a complete, explicit description of the inertial Weil--Deligne types arising from elliptic curves over $Q_{ℓ}$ for $ℓ$ prime.

On Fermat-type equations of signature (r,r,p)

Congruences and ramified primes in fields of coefficients of newforms

On Darmon's program for the Generalized Fermat equation, II

Two results on xr+yr=dzp

On Darmon's program for the generalized Fermat equation, I

On Galois inertial types of elliptic curves over Qℓ​

On Fermat-type equations of signature $(r, r, p)$

Two results on $x^{r} + y^{r} = d z^{p}$

On Galois inertial types of elliptic curves over $Q_{ℓ}$