Correlations of multiplicative functions and rational points in families

Time: Wed 2019-05-29 11.00

Lecturer: Lilian Matthiesen, Institutionen för Matematik

Location: F11, Lindstedtsvägen 22, F-huset, våningsplan 2, KTH Campus

Abstract

This talk will be about two recently completed and very different research projects that are nonetheless connected to each other. 

In the first part of the talk I will discuss a general asymptotic result on certain correlations of multiplicative functions and its background. In the simplest instance, these correlations take the form sum_{n,d < x} h_1(n) h_2(n+d) ... h_{r+1}(n+rd), where h_1, ..., h_{r+1} are multiplicative functions. I will describe a set of conditions under which such correlations can be evaluated asymptotically as well as examples of functions satisfying these conditions. 

The second part of the talk will be about joint work with Dan Loughran on a question of Serre. By combining the analytic result on multiplicative functions mentioned above with ideas from algebraic geometry, we obtain (under suitable conditions) correct-order lower bounds for the number of varieties in a family over Q which have a rational point.

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Last changed: May 10, 2019