14 citations · 54 across the 30 of their papers we have counts for
32 papers
K-varieties and Galois representations
Enric Florit, Ariel Pacetti
In a remarkable article Ribet showed how to attach rational -dimensional representations to elliptic -curves. An abelian variety is a (weak) -variety if it i…
On the -Selmer group of Jacobians of hyperelliptic curves
Daniel Barrera Salazar, Ariel Pacetti, Gonzalo Tornaría
Let be a hyperelliptic curve defined over a number field with integral of odd degree. The purpose of the present article is to prove lower and…
On computing finite index subgroups of PSL(2,Z)
Nicolás Mayorga Uruburu, Ariel Pacetti, Leandro Vendramin
We present a method to compute finite index subgroups of . Our strategy follows Kulkarni's ideas, the main contribution being a recursive method to compute bival…
On endomorphism algebras of -type abelian varieties and Diophantine applications
Franco Golfieri Madriaga, Ariel Pacetti, Lucas Villagra Torcomian
Let and be two different newforms without complex multiplication having the same coefficient field. The main result of the present article proves that a congruence between…
Quinary forms and paramodular forms
Neil Dummigan, Ariel Pacetti, Gustavo Rama +1
We work out the exact relationship between algebraic modular forms for a two-by-two general unitary group over a definite quaternion algebra, and those arising from genera of posit…
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…