Publications and preprints

All the codes used in the papers are available at https://github.com/lucasvillagra. The versions posted in arxiv may not be in final form, please see the published versions.

1. On the conductor of a family of Frey hyperelliptic curves, with Pedro-José Cazorla García.
   Submitted [arXiv].

2. On the sum of fifth powers in arithmetic progression.
   The Ramanujan Journal, Vol. 68, No. 29 (2025). [DOI | arXiv].

3. On endomorphism algebras of GL_2-type abelian varieties and Diophantine applications, with Franco Golfieri and Ariel Pacetti.
   Revista Matemática Iberoamericana,  Vol. 41, No. 5 (2025), pp. 1897–1924.  [DOI | arXiv].

4. Asymptotic Fermat for signature (4,2,p) over number fields.
   Journal of Number Theory, Vol. 250 (2023),  pp. 124-138 [DOI | arXiv].

5. On the equation x²+dy⁶=zp for square-free 1≤d≤20, with Franco Golfieri and Ariel Pacetti.
   International Journal of Number Theory, Vol. 19, No. 05 (2023), pp. 1129-1165 [DOI | arXiv].

6. Q-curves, Hecke characters and some Diophantine equations II, with Ariel Pacetti.
   Publicacions Matemàtiques, Vol. 67, No. 2 (2023),  pp. 569-599 [DOI | arXiv].

7. Q-curves, Hecke characters and some Diophantine equations, with Ariel Pacetti.
   Mathematics of Computation, Vol. 91, No. 338 (2022),  pp.  2817-2865 [DOI | arXiv].

Other surveys (in Spanish)

• Q-curvas y caracteres de Hecke en el método modular, PhD Thesis (pdf)

• Correspondencia de Langlands en dimensión 1, trabajo final de licenciatura (pdf)

• Teorema de Lax-Milgram y aplicaciones al método de elementos finitos, with Agustina Czenky, concurso de monografía de la UMA (pdf)