5 papers
On the generalized Fermat equation of signature
Ariel Pacetti, Lucas Villagra Torcomian
In this article we study solutions to the generalized Fermat equation using hypergeometric motives within the framework of the modular method. In doing so, we give…
A note on conductors of Frey representations at
Imin Chen, Lucas Villagra Torcomian
In 2000, Darmon introduced the notion of Frey representations within the framework of the modular method for studying the generalized Fermat equation. A central step in this progra…
On the conductor of a family of Frey hyperelliptic curves
Pedro-José Cazorla García, Lucas Villagra Torcomian
In his breakthrough article, Darmon presented a program to study Generalized Fermat Equations (GFE) via abelian varieties of -type over totally real fields. So far, on…
Asymptotic Fermat for signature over number fields
Lucas Villagra Torcomian
Let be a number field. Using the modular method, we prove asymptotic results on solutions of the Diophantine equation over , assuming some deep but standard co…
On the equation for square-free
Franco Golfieri, Ariel Pacetti, Lucas Villagra Torcomian
The purpose of the present article is to show how the modular method together with different techniques can be used to prove non-existence of primitive non-trivial solutions of the…