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# 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
Tags/Keywords
• von Mongoldt function

• Multiplicative functions

• divisor functions

• correlation sums

• shifted convolution sums

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### Matomäki

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 $|h| \leq (\log X)^{O_{k, l} ( 1) }$.

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