New Website
I have a new website with updated information, and links to apps I am building. Please check it out! This old website will no longer be updated, and it will disappear at some point in the near future.
About me
- I'm a Professor of Mathematics at the University of Connecticut.
- Information about CTNT - Connecticut Summer School in Number Theory.
- A video survey of my research area at CIRM (Luminy, France), and my VaNTAGe talk on ranks of elliptic curves.
- Books that I have published: AMS books, see also this page about "Number Theory and Geometry."
- My YouTube channel (mini-courses and lectures).
- My Blog: A Field Guide To Mathematics.
- Álvaro in the media.
Contact Info
| Phone: | (860) 486 3850 |
|---|---|
| E-mail: | alvaro.lozano-robledo@uconn.edu |
| Address: | MONT 233 Department of Mathematics University of Connecticut 341 Mansfield Road U1009 Storrs, CT 06269-1009 USA |
Elliptic curve addition and doubling of rational points.
Selected Publications
Books :
- Number Theory and Geometry: An Introduction to Arithmetic Geometry, AMS, Pure and Applied Undergraduate Texts, Book 35, 2019.
- Elliptic Curves, Modular Forms and Their L-functions, AMS, Student Mathematical Library, Vol. 58, 2011.
Selected Articles (all preprints and offprints are available here):
- Galois representations attached to elliptic curves with complex multiplication, in Algebra and Number Theory, 16:4 (2022). (arXiv preprint: 1809.02584.)
- A probabilistic model for the distribution of ranks of elliptic curves over Q, in Journal of Number Theory, Volume 221, April 2021, 270-338. (arXiv preprint: 1611.01999; see also my VaNTAGe talk on this topic.)
- Uniform boundedness in terms of ramification, in Research in Number Theory, 2018, 4:6.
- Torsion subgroups of rational elliptic curves over the compositum of all cubic fields (with Harris Daniels, Filip Najman, and Andrew Sutherland), arXiv preprint: 1509.00528 (current version corrects an error in the proofs of Lemma 3.2 and Theorem 3.6), in Mathematics of Computation, 87 (2018), 425-458.
- On the minimal degree of definition of p-primary torsion subgroups of elliptic curves (with Enrique González-Jiménez), in Mathematical Research Letters., Vol 24 (2017), Num. 4, pp. 1067-1096. Magma scripts.
- What is... an elliptic curve? (with Harris Daniels), in the Notices of the American Mathematical Society., Vol 64, Issue 3, March 2017, pp. 241-243.
- Elliptic curves with abelian division fields (with Enrique González-Jiménez), in Mathematische Zeitschrift, August 2016, Volume 283, Issue 3, pp. 835–859.
- Ramification in the division fields of elliptic curves with potential supersingular reduction, in Research in Number Theory 2016 2:8, pp. 1-25.
- Division fields of elliptic curves with minimal ramification, in the Revista Matematica Iberoamericana, Volume 31, Issue 4, 2015, pp. 1311–1332.
- On the field of definition of p-torsion points on elliptic curves over the rationals, in the Mathematische Annalen, Vol 357, Issue 1 (2013), pp. 279-305.
- On products of quadratic twists and ranks of elliptic curves over large fields (joint with Bo-Hae Im), in Journal of the London Mathematical Society, Vol 79, part 1, Feb. 2009, pp. 1-14.