Research Publications (2004-2007):

1. Ranks of abelian varieties over infinite extensions of the rationals, to appear in Manuscripta Mathematica.

2. Bernoulli-Hurwitz numbers, Wieferich primes and Galois representations, submitted.

3. On products of quadratic twists and ranks of elliptic curves over large fields (joint with Bo-Hae Im), submitted.

4. Elliptic curves of maximal rank, (joint work with Julian Aguirre and Juan Carlos Peral), submitted.

5. On the product of twists of rank two and a conjecture of Larsen, to appear in the Ramanujan Journal.

6. Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion, in RACSAM (Journal of the Royal Academy of Science of Spain),
Vol 101 (1), 2007.

7. Constructing elliptic curves over Q(t) with moderate rank, (joint with Scott Arms and Steven J.Miller), Journal of Number Theory, Volume 123, Issue 2, April 2007, 388-402.

8. On elliptic units and p-adic Galois representations attached to elliptic curves, Journal of Number Theory, Vol. 117, Issue 2, (2006), 439-470.

9. On the surjectivity of Galois representations attached to elliptic curves over number fields, Acta Arithmetica, Vol. 117, No. 3, (2005), 283-291.

10. On certain closed subgroups of SL(2,Z_p[[X]]), Revista Colombiana de Matemáticas, Vol 39 (2005), pp. 13-19.

11. Buscando puntos racionales en curvas elípticas: Métodos explícitos, La Gaceta de la Real Sociedad Matematica Española (J. of the Royal Mathematical Society of Spain), Vol. 8 (2005), n 2, 471-488.