9 citations · 21 across the 8 of their papers we have counts for
7 papers · 1 filter
New algebraic points on covers of elliptic curves
Diana Mocanu, George C. Turcas
For a smooth projective curve of genus and an extension, we write . Recent work of Khawaja a…
Transversal Difference Numbers in Finite Abelian Quotients
Mugurel Barcau, Vicenţiu Paşol, George C. Ţurcaş
Given \(H\leq G\) finite abelian groups, a transversal \(T\subseteq G\) for \(G/H\) has fixed size \(|G/H|\), but its ambient difference support \(D(T)=T-T\) can vary with the embe…
Logarithmic Density of Rank and Rank Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography
Razvan Barbulescu, Mugurel Barcau, Vicentiu Pasol +1
In this work we study quantitative existence results for genus- curves over whose Jacobians have Mordell--Weil rank at least or , ordering the curves by the…
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…
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…
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)=…
On Fermat's equation over some quadratic imaginary number fields
George Turcas
Assuming a deep but standard conjecture in the Langlands programme, we prove Fermat's Last Theorem over . Under the same assumption, we also prove that, for all prime…