## Number Theory Seminar

### Tuesday, March 12th, 2019

**Time:** 1:00-2:00 p.m. **Place:** Jeffery Hall 422

**Speaker:** Arpita Kar (Queen's University)

**Title:** On the normal number of prime factors of Euler Phi function at shifts of prime arguments.

**Abstract:** Let $\omega(n)$ and $\Omega(n)$ denote the number of prime factors of a natural number $n$ counted without and with multiplicity respectively. Let $\phi(n)$ denote the Euler totient function. In 1984, R.Murty and K. Murty defined a certain class of multiplicative functions and computed the normal order of $\omega(f(p))$ and $\omega(f(n))$ for $f$ belonging in that class. An example of functions in this class is $\phi(n)$. In this talk, we will discuss the normal number of prime factors of $\phi(n)$ at shifts of prime arguments, that is, $\Omega(\phi(p+a))$, for primes $p$ and any non-zero integer $a$.

This is joint work with Prof. Ram Murty.