Ranks of elliptic curves in quadratic twist families via Iwasawa theory

Abstract: For a fixed elliptic curve $E/\mathbb{Q}$, Goldfeld's Conjecture predicts that half of its quadratic twists have rank 0 and half have rank 1. This conjecture is now a theorem in most cases, due to recent work of Alex Smith. However, it is still interesting to ask for effective versions of this theorem; for instance, if one considers only twists by prime numbers which are 1 mod 4, what can be said about the rank distribution? In this talk, we will discuss joint work with Anwesh Ray which uses Iwasawa theory to study some of these sorts of questions.

number theory

Audience: researchers in the topic

( paper )

Five College Number Theory Seminar