Thursday 12 Apr 2018Number 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.

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