Class numbers of imaginary quadratic fields

Posted on: March 20, 2017




Olivia Beckwith
Emory University

Thursday, March 23, 2017
Manchester 020, 11:00am

Class Numbers of Imaginary Quadratic Fields

Abstract: Ideal class groups measure the departure of the ring of integers of a number field from being a Unique Factorization Domain. I will discuss what is known and what is conjectured about the structure of class groups, and why there is a big gap between the two. Then I will describe a result in which I quantify a recent theorem of Wiles by proving an estimate for the number of negative fundamental discriminants down to -X whose class numbers are indivisible by a give prime and whose imaginary quadratic fields satisfy almost any given finite set of local conditions. This estimate matches the best results in the direction of the Cohen-Lenstra heuristics for the number of imaginary quadratic fields with class number indivisible by a given prime. I will also discuss an application to rank 0 twists of certain elliptic curves.

Host: Jeremy Rouse,