Thursday 12 Apr 2018: Number Theory Seminar: An analogue of the Erd?s-Kac theorem for the special linear group over the integers
Daniel El-Baz - Tel-Aviv University
Laver LT6 14:30-15:30
The Erd?s-Kac theorem (1940) can be viewed as marking the birth of probabilistic number theory. It asserts a central limit theorem for the number of prime factors of integers.
I will discuss a possible analogue of this theorem for certain algebraic varieties over the rationals. As a 'proof of concept', I will present the case of the special linear group over the integers. The method employs homogeneous dynamics to establish a level of distribution result that can be fed into a classical sieve theoretic framework. This is based on work in progress with Efthymios Sofos.