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Session S21 - Galois representations and automorphic forms

No date set.

Using Q-curves and Hecke characters to solve Fermat-type equations

Lucas Villagra Torcomian

Universidad Nacional de Córdoba, Argentina   -   lucas.villagra@mi.unc.edu.ar

In this poster we wil see how can we adapt the classical modular method using Q-curves and Hecke characters in order to solve the diophantine equations x4+dy2=zp and x2+dy6=zp. The results obtained are in [1] and [2].

[1] Ariel Pacetti and Lucas Villagra Torcomian. Q-curves, hecke characters and some diophantine equations, 2020.

[2] Ariel Pacetti and Lucas Villagra Torcomian. Q-curves, hecke characters and some diophantine equations II, 2021.

Joint work with Ariel Pacetti (Center for Research and Development in Mathematics and Applications).

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