Logo

Mathematical Sciences Research Institute

Home » Workshop » Schedules » Correlations of von Mangoldt and higher order divisor functions

Correlations of von Mangoldt and higher order divisor functions

Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017

May 03, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Kaisa Matomäki (University of Turku)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

I will discuss joint work with M. Radziwill and T. Tao on asymptotics for the sums $\sum_{n \leq x} \Lambda(n) \Lambda(n+h)$ and $\sum_{n \leq x} d_k(n) d_l(n+h)$ where $\Lambda$ is the von Mangoldt function and $d_k$ is the kth divisor function. For the first sum we show that the expected asymptotics hold for almost all $|h| \leq X^{8/33}$ and for the second sum we show that the expected asymptotics hold for almost all $|h| \leq (\log X)^{O_{k, l} ( 1) }$.

Supplements
28396?type=thumb Matomaki Notes 1.22 MB application/pdf Download
Video/Audio Files

Matomäki

H.264 Video 8-Matomäki.mp4 554 MB video/mp4 rtsp://videos.msri.org/data/000/028/315/original/8-Matoma%CC%88ki.mp4 Download
Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.

See more of our Streaming videos on our main VMath - Streaming Video page.