3 citations · 5 across the 5 of their papers we have counts for
5 papers
Proving modularity for a given elliptic curve over an imaginary quadratic field
Luis Dieulefait, Lucio Guerberoff, Ariel Pacetti
We present an algorithm to determine if the -series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agr…
Solving Fermat-type equations x^5+y^5=dz^p
Nicolas Billerey, Luis Dieulefait
In this paper we are interested in solving the Fermat-type equations x^5+y^5=dz^p where d is a positive integer and p a prime number . We describe a new method based on modu…
Congruences between modular forms and lowering the level mod l^n
Luis Dieulefait, Xavier Taixes i Ventosa
In this article we study the behavior of inertia groups for modular Galois mod l^n representations and in some cases we give a generalization of Ribet's lowering the level result
Small primitive roots and malleability of RSA moduli
Luis Dieulefait, Jorge Jimenez Urroz
In a paper of P. Paillier and J. Villar a conjecture is made about the malleability of an RSA modulus. In this paper we present an explicit algorithm refuting the conjecture. Concr…
How to facet a gemstone: from potential modularity to the proof of Serre's modularity conjecture
Luis Dieulefait
In this survey paper we present recent results obtained by Khare, Wintenberger and the author that have led to a proof of Serre's conjecture, such as existence of compatible famili…