Nathan Jones : The distribution of class groups of imaginary quadratic fields

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

At

April 21, 2015, 11 a.m.

In

SEO 427

Abstract

Which abelian groups occur as the class group of some imaginary quadratic field? Inspecting tables of M. Watkins on imaginary quadratic fields of class number up to 100, one finds that some abelian groups do not occur as the class group of any imaginary quadratic field (for instance (Z/3Z)^3 does not). In this talk, I will combine heuristics of Cohen-Lenstra together with a refinement of a conjecture of Soundararajan to make precise predictions about the asymptotic distribution of imaginary quadratic class groups, partially addressing the above question. I will also present some numerical evidence of the resulting conjectures. This is based on joint work with S. Holmin, P. Kurlberg, C. Macleman, and K. Petersen.