Ramin Takloo-Bighash : Counting subrings of Z^n

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

Sept. 19, 2011, 3 p.m.

In

SEO 612

Abstract

In this talk I will explain a method, based on p-adic integration, to count the number of subrings of ${\mathbb Z}^n$ of bounded additive index. The method yields exact asymptotic formulae for small $n$, and gives non-trivial bounds for all $n$. At the end I will explain how this method could be applied to the problem of counting orders in quintic fields. This is joint work with Nathan Kaplan.