Research

Papers

Tables

Software




logo UAM

Research:

Number Theory: Elliptic curves, Hyperelliptic curves, Modular curves, Q-curves, Modular Abelian Varieties, Arithmetic progressions.

Papers:

  1. Five squares in arithmetic progression over quadratic fields (joint with X. Xarles). Submitted. pdf and data. arXiv: 0909.1663

  2. On symmetric square values of quadratic polynomials (joint with X. Xarles). Acta Arithmetica 149, 145-159 (2011) pdf web data.
  3. On fields of definition of torsion points of elliptic curves with complex multiplication (joint with L. Dieulefait and J. Jiménez Urroz). Proceeding of the American Mathematical Society 139, no. 6, 1961-1969 (2011). pdf data doi
  4. Three cubes in arithmetic progression over quadratic fields. Archiv der Mathematik Vol. 95, no. 3, 233-241 (2010). pdf doi
  5. On the ubiquity of trivial torsion on elliptic curves (joint with J.M. Tornero). Archiv der Mathematik Vol. 95, no. 2, 135-141 (2010). pdf doi
  6. Arithmetic progressions of four squares over quadratic fields (joint with J. Steuding). Publicationes Mathematicae Debrecen 77, 1-2, 125-138 (2010). pdf web
  7. On the modularity level of modular abelian varieties over number fields (joint with X. Guitart). Journal of Number Theory 130, no. 7, 1560-1570 (2010). pdf doi
  8. 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 doi
  9. Non-hyperelliptic modular curves of genus 3 (joint with R. Oyono). Journal of Number Theory 130, no. 4, 862-878 (2010). pdf doi
  10. Right triangles with algebraic sides and elliptic curves over number fields (joint with E. Girondo, G. González-Diez, R. Steuding and J. Steuding). Mathematica Slovaca 59, no. 3, 299-306 (2009). pdf doi
  11. Finiteness Results for modular curves of genus at least 2 (joint with M. Baker, J. González and B. Poonen). American Journal of Mathematics 127, no. 6, 1325-1387, (2005). pdf doi
  12. On the Brauer class of modular endomorphism algebras (joint with E. Ghate and J. Quer). International Mathematics Research Notices 2005 no. 12, 701-723, (2005). pdf doi
  13. Modular curves of genus 2 (joint with J. González). Mathematics of Computation 72, no. 241, 397—418, (2003). pdf doi data
  14. 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 doi
  15. Curves of genus 2 parametrized from modular curves (joint with J. González). Actas EACA VII, 177-185 (2001).

Books:

  1. 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.
  2. Curvas Hiperelípticas Modulares. Ph.D.thesis (in Spanish), January 2002. Abstract: English, Spanish
  3. 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:16/6/2011