Research

Papers

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Research:

Number Theory: Elliptic curves, Hyperelliptic curves, Modular curves, Q-curves, Modular Abelian Varieties, Arithmetic progressions.
Cryptography: Public key cryptography: ECC, RSA.

Papers:

  1. On symmetric square values of quadratic polynomials (joint with X. Xarles). Submited. pdf and data. arXiv: 1001.4710
  2. On the ubiquity of trivial torsion on elliptic curves (joint with J.M. Tornero). Submited. pdf. arXiv: 1002.0667
  3. On the modularity level of modular abelian varieties over number fields (joint with X. Guitart). Submited. pdf. arXiv: 1002.0492
  4. On fields of definition of torsion points of elliptic curves with complex multiplication (joint with L. Dieulefait and J. Jiménez Urroz). Submited. pdf and data. arXiv: 0909.1661
  5. Five squares in arithmetic progression over quadratic fields (joint with X. Xarles). Submited. pdf and data. arXiv: 0909.1663
  6. Three cubes in arithmetic progression over quadratic fields. Submited. pdf. arXiv: 0909.0227

  7. Arithmetic progressions of four squares over quadratic fields (joint with J. Steuding). To appear at Publ. Math. Debrecen. pdf. arXiv: 0903.3856
  8. Non-hyperelliptic modular curves of genus 3 (joint with R. Oyono). Journal of Number Theory 130, no. 4, 862-878 (2010). pdf
  9. Galois theory, discriminants and torsion subgroup of elliptic curves (joint with I. García-Selfa and J.M. Tornero). Journal of Pure and Applied Algebra 214, 1340-1346 (2010). pdf
  10. Right triangles with algebraic sides and elliptic curves over number fields (joint with E. Girondo, G. González-Diez, R. Steuding and J. Steuding). Math. Slovaca 59, no. 3, 299-306 (2009). pdf
  11. Finiteness Results for modular curves of genus at least 2 (joint with M. Baker, J. González and B. Poonen). Amer. J. Math. 127, no. 6, 1325-1387, (2005). pdf
  12. On the Brauer class of modular endomorphism algebras (joint with E. Ghate and J. Quer). Int. Math. Res. Not. 2005, no. 12, 701-723, (2005). pdf
  13. Computations on Modular jacobians surfaces (joint with J. González and J. Guàrdia). Algorithmic number theory (Sydney, 2002), 189-197, LNCS 2369, Springer, Berlin, (2002). pdf
  14. Modular curves of genus 2 (joint with J. González). Math. Comp. 72, no. 241, 397—418, (2003). pdf, data
  15. Curves of genus 2 parametrized from modular curves (joint with J. González). Actas EACA VII, 177-185 (2001).

Books:

  1. Introducción a la modularidad de curvas elípticas: Un enfoque teórico-computacional (joint with A. Pérez). Ediciones IVIC (2010). ISBN 978-980-261-XXX-X (In progress).
  2. Proceedings of the Segundas Jornadas de Teoría de Números (joint with J. Cilleruelo, A. Quirós, X. Xarles (eds.)). Biblioteca de la Revista Iberoamericana de Matemáticas vol. 4 (2008). ISBN 978-84-612-8007-0.
  3. Curvas Hiperelípticas Modulares. Ph.D.thesis (in Spanish), January 2002. Abstract: English, Spanish
  4. Curvas elípticas: Grupo de puntos racionales y curvas de rango alto. Master thesis (in Spanish), January 1998. pdf

Tables:

Software (MAGMA):

Conference Organizer:

Last modified:8/3/2010