3 citations · 3 across the 4 of their papers we have counts for
14 papers
Sum of consecutive powers as a perfect power
Angelos Koutsianas, Nikos Tzanakis
In this paper we study the equation when . We prove that the only solutions are for when or…
The generalized Fermat equation and applications
Pedro-José Cazorla García, Angelos Koutsianas, Lucas Villagra-Torcomian
In this paper, we develop the modular method for the generalized Fermat equation appearing in the title, within the framework of Darmon's program and using Frey hyperelliptic curve…
Darmon's Program: A survey
Imin Chen, Angelos Koutsianas
We give an overview of Darmon's program for resolving families of generalized Fermat equations with one varying exponent and survey what is currently known about this approach base…
Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
Stevan Gajović, Jeroen Hanselman, Angelos Koutsianas
In this paper, we prove that the local-global principle of -isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by B…
A modular approach to Fermat equations of signature using Frey hyperelliptic curves
Imin Chen, Angelos Koutsianas
In this paper we carry out the steps of Darmon's program for the generalized Fermat equation In particular, we develop the machinery necessary to prove an op…
Weak Approximation for -cycles on a product of elliptic curves
Evangelia Gazaki, Angelos Koutsianas
In the 1980's Colliot-Thélène, Sansuc, Kato and S. Saito proposed conjectures related to local-to-global principles for -cycles on arbitrary smooth projective varieties over a n…