Lethbridge Number Theory and Combinatorics Seminar: Po-Han Hsu

Let omega(n) denote the number of distinct prime divisors of n. Let W(m) be a random integer chosen uniformly from the set of natural numbers less than or equal to m. Let X(m) be omega(W(m)). The celebrated Erdos-Kac theorem asserts that if the difference X(m) - log log m is divided by the square root of log log m, then the limit of this quotient is the standard normal distribution.

In 2016, Mehrdad and Zhu studied the large and moderate deviations for the Erdos-Kac theorem. In this talk, we will give a brief introduction to the theory. Then we will discuss how to establish the large deviation principle for X(m)/(log log m). If time allows, we will discuss some generalisations.

This is a joint work with Dr Peng-Jie Wong.