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Ranks of elliptic curves twisted by thin sets
Algebraic Geometry and Number Theory| Speaker: | Cihan Sabuncu, MPIM Bonn |
| Related Webpage: | https://sites.google.com/view/cihan-sabuncu/home?pli=1&authuser=0 |
| Location: | 2112 MSB |
| Start time: | Thu, Oct 22 2026, 11:00AM |
Description
Let $E$ be an elliptic curve over the rationals, and let $E^d$ be its twist by the quadratic character $\chi_d$. Information about the ranks of $E^d$ is an important question in Number Theory, and, besides its intrinsic importance, one reason is its deep connection to the Birch and Swinnerton-Dyer conjecture. Restricting the twists to be in thinner sets is likewise an important but more difficult question. In this talk, I will show that there are infinitely many twists d which are sums of two squares such that $E^d$ has rank 1. This is joint work with Mohammad H. Hamdar.