Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Number Theory Seminar


Wednesday, May 15th, 2019

Time: 3:30-4:30 p.m.  Place: Jeffery Hall 319

Speaker: Anup Dixit (Queen's University)

Title: On the distribution of the number of local prime factors of n

Abstract: Let $\omega(n)$ denote the number of distinct prime factors of $n$ and $\omega_y(n)$ denote the number of distinct prime factors of $n$ less than $y$. It was shown by Hardy and Ramanujan that typically $\omega(n)$ is $\log \log n$ up to an error term of $\sqrt{\log \log n}$. This was further generalized in the famous Erd\"{o}s-Kac theorem, which asserts that the probability distribution of $(\omega(n) - \log \log n)/(\sqrt{\log\log n})$ is the standard normal distribution.In this talk, we will prove analogous results for $\omega_y(n)$, which can be thought of as a local Erd\"{o}s-Kac theorem and describe its further implications. This is joint work with Prof. Ram Murty.