11 citations · 18 across the 9 of their papers we have counts for
4 papers · 2 filters
On some remarkable congruences between two elliptic curves
Nicolas Billerey
We exhibit two non-isogenous rational elliptic curves with -torsion subgroups isomorphic as Galois modules.
Strong modularity of reducible Galois representations
Nicolas Billerey, Ricardo Menares
In this paper, we call strongly modular those reducible semi-simple odd mod Galois representations for which the conclusion of the strongest form of Serre's original modularity…
A result on the equation using Frey abelian varieties
Nicolas Billerey, Imin Chen, Luis Dieulefait +1
We prove a diophantine result on generalized Fermat equations of the form which for the first time requires the use of Frey abelian varieties of dimension $\geq 2…
Sums of two -units via frey-hellegouarch curves
Michael Bennett, Nicolas Billerey
In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is…