3 papers
math.NT2020
Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields
Filip Najman, George C. Turcas
In this note we prove that for every integer , there exists an explicit constant such that the following holds. Let be a number field of degree , let $q > \m…
math.NT2019
On Serre's modularity conjecture and Fermat's equation over quadratic imaginary fields of class number one
George Catalin Turcas
In the present article, we extend previous results of the author and we show that when is any quadratic imaginary field of class number one, Fermat's equation d…
math.NT2018
Irreducible binary cubics and the generalized superelliptic equation over number fields
George Catalin Turcas
For a large class (heuristically most) of irreducible binary cubic forms , Bennett and Dahmen proved that the generalized superelliptic equation $F(x,y)=…