Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

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.