Random multiplicative functions: progress and problems

Abstract: A random multiplicative function is a random function on the natural numbers, that is constructed from a sequence of independent random variables in a way that respects the multiplicative structure. These objects arise naturally in analytic number theory as models for things like Dirichlet characters, but can also be thought of simply as probabilistic objects with an interesting dependence structure. In this talk I will try to survey what we know about random multiplicative functions, and some open problems, in a way that is (hopefully) accessible and interesting to number theorists, probabilists, and others.

Mathematics

Audience: general audience

Heilbronn Annual Conference 2020