# Queen's University - Department of Mathematics and Statistics

 Wednesday, November 8 Number Theory Seminar Time: 1:30 p.m. Place: Jeffery 319 Speaker: Francesco Cellarosi Title: Smooth Sums over Smooth k-Free Integers Abstract Attached Friday, November 10 Remembrance Day Services Time: 10:30 a.m. Place: Grant Hall Classes cancelled 10:30 am – 11:30 am Friday, November 10 Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 Speaker: Hector Pasten, Harvard University Title: In Quest of Arithmetic Derivatives Abstract Attached Friday, November 24 Ph.D. Thesis Defense Time: 10:00 a.m. Place: Jeffery 521 Ph.D. Student: Aaron Springford Title: Spectral analysis of time series with latent and irregular times Supervisors: D. Thomson and G. Takahara

Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.

Wednesday, November 8, 1:30 p.m. Jeffery 319 - Number Theory Seminar

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.

Friday, November 10, 2:30 p.m. Jeffery 234 - Department Colloquium

Speaker: Hector Pasten

Title: In Quest of Arithmetic Derivatives

Abstract: There are well-known arithmetic analogies between integers and polynomials (or more generally, holomorphic functions), specially with respect to solutions of Diophantine equations. A crucial aspect that is missing in this analogy is that for polynomials and holomorphic functions one can use derivatives, while for integers there is no direct substitute of this operation. After some motivation, I will discuss a couple of possible candidates for arithmetic derivatives.

### Contact Info

 Department of Math & Stats Jeffery Hall, 48 University Ave. Kingston, ON Canada, K7L 3N6 Phone: (613) 533-2390 Fax: (613) 533-2964 mathstat@mast.queensu.ca Office Hours: 8:30am-12:00pm & 1:00pm-4:30pm