Nathan Jones : Cohen-Lenstra heuristics

Posted by Nathan Jones , part of the Number Theory Seminar.

At

Feb. 17, 2015, 11 a.m.

In

SEO 427

Abstract

If the class number of an imaginary quadratic field behaved like a random positive integer, then the asymptotic proportion of class numbers which are divisible by 3 would be 1/3, or about 33.3%. However, this proportion is observed to be around 43%. In this talk, I will survey heuristic reasoning due to Cohen-Lenstra from the 1980s which explains this phenomenon and makes various other precise statistical predictions about class groups.