4 papers
On rank hypergeometric motives
Franco Golfieri Madriaga, Ariel Pacetti, Fernando Rodriguez Villegas
Hypergeometric motives are family of motives associated to hypergeometric local systems. Their special features, in particular their rigidity, makes them more tractable than genera…
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…
Hypergeometric motives and the generalized Fermat equation
Franco Golfieri Madriaga, Ariel Pacetti
In the beautiful article [11] Darmon proposed a program to study integral solutions of the generalized Fermat equation . In the aforementioned article, Darmon prove…
On Transformation properties of hypergeometric motives and Diophantine equations
Ariel Pacetti
Over the last two hundred years different transformation formulas for Gauss' hypergeometric function were discovered. The goal of the present article is to study their ar…