Ariel Pacetti

activity

20032024

most citedTheta Lifts of Bianchi Modular Forms and Applications to Paramodularity

14 citations · 54 across the 30 of their papers we have counts for

collaborators

Showing 2020 · math.NTShow all

3 papers · 2 filters

math.NT2020

On Galois representations of superelliptic curves

Ariel Pacetti, Angel Villanueva

A superelliptic curve over a DVR $O$ of residual characteristic $p$ is a curve given by an equation $C : y^{n} = f (x)$ . The purpose of the present article is to describe the G…

math.NT2020

$Q$ -curves, Hecke characters and some Diophantine equations

Ariel Pacetti, Lucas Villagra Torcomian

In this article we study the equations $x^{4} + d y^{2} = z^{p}$ and $x^{2} + d y^{6} = z^{p}$ for positive square-free values of $d$ . A Frey curve over $Q (- d)$ is attached to each primi…

math.NT2020

On $2$ -Selmer groups and quadratic twists of elliptic curves

Daniel Barrera Salazar, Ariel Pacetti, Gonzalo Tornaría

Let $K$ be a number field and $E / K$ be an elliptic curve with no $2$ -torsion points. In the present article we give lower and upper bounds for the $2$ -Selmer rank of $E$ in terms o…

On Galois representations of superelliptic curves

Q-curves, Hecke characters and some Diophantine equations

On 2-Selmer groups and quadratic twists of elliptic curves

$Q$ -curves, Hecke characters and some Diophantine equations

On $2$ -Selmer groups and quadratic twists of elliptic curves