# Best approximation by restricted divisor sums and random matrix integrals

## Location

383N

Event Series

Event Type

Seminar

Monday, February 12, 2024 2:30 PM

Brad Rodgers (Queens)

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.