Brad Rodgers: Best approximation by restricted divisor sums and random matrix integrals

Speaker
Brad Rodgers, Queens University

Abstract
Let X be large and H also large but slightly smaller, and consider n ranging from 1 to X. For an arithmetic function f(n) like the k-fold divisor function, what is the best mean square approximation of f(n) by a restricted divisor sum (a function of the sort \(\sum_{d|n, d < H} a_d\))? I hope to explain some of the context around this question and how the answer is connected to random matrix integrals over the unitary group.