## Number Theory Seminar

### Wednesday, November 8th, 2017

**Time:** 1:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Francesco Cellarosi

**Title:** Smooth Sums over Smooth k-Free Integers

**Abstract:** We provide an asymptotic estimate for certain sums over k-free integers with small prime factors. These sums depend upon a complex parameter $\alpha$ and involve a smooth cut-off $f$. They are a variation of several classical number-theoretical sums. One term in the asymptotics is an integral operator whose kernel is the $\alpha$-convolution of the Dickman-de Bruijn distribution, and the other term is explicitly estimated. The trade-off between the value of $\alpha$ and the regularity of $f$ is discussed.