## Lethbridge Number Theory and Combinatorics Seminar: Lee Troupe

- Date: 10/16/2017

University of Lethbridge

Normally Distributed Arithmetic Functions

In the late 1930s, Paul Erdos attended a seminar at Cornell University given by Mark Kac, who suspected that divisibility by primes satisfies a certain "statistical independence" condition. If this were true, the central limit theorem could be used to show that the number of distinct prime factors of n, as n varies over the natural numbers, is normally distributed, with mean loglogn and standard deviation the square root of log log n. Erdos used sieve methods to confirm Kac's intuition, and the resulting Erdos-Kac theorem is a foundational result in the field of probabilistic number theory. Many different proofs of and variations on the Erdos-Kac theorem have been given in the intervening decades. This talk will highlight some of these results and the techniques used to obtain them, including recent work of the speaker and Greg Martin (UBC).