Adam Harper

High moments of random multiplicative functions

Random multiplicative functions $f(n)$ are a probabilistic model for certain interesting number theoretic functions, such as the Mobius function and Dirichlet characters. When $0 \leq q \leq 1$, it turned out that the moments $\E|\sum_{n \leq x} f(n)|^{2q}$ were connected with the notion of multiplicative chaos from physics and probability. In this talk, I will discuss the behaviour of the moments in the other regime where $q > 1$. Here one sees some other interesting phenomena, especially for Rademacher random multiplicative functions where there is a "unitary to orthogonal" transition as $q$ grows.