# Divisor sums in short intervals

## Brad Rodgers(University of Michigan)

In this talk we will discuss recent joint work with Jon Keating, Edva Roditty-Gershon, and Zeev Rudnick regarding the distribution sums of the k-fold divisor function over short intervals. This distribution is closely related to moments of the Riemann zeta function. We will talk about new conjectures for the variance of these sums, which have several surprising features, and also discuss an analogous result in a function field setting which motivates the conjectures and which may be proved by using, in part, random matrix theory. If there is sufficient time we will discuss a decomposition of arithmetic functions that elucidates some of the surprising features we will have talked about.

Tuesday, November 22, at 4:00pm in HBH 227

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