**Title:** Rational sets, polynomial multiple recurrence and applications to multiplicative number theory

**Speaker:** Florian Richter

**Speaker Info:** Ohio State University

**Brief Description:**

**Special Note**:

**Abstract:**

A subset of the natural numbers is called rational if it is well approximable (in upper density) by finite unions of arithmetic progressions. Rational sets arise naturally in multiplicative number theory. Examples of rational sets include the squarefree numbers, the abundant numbers, sets of B-free numbers and many more.In my talk we will consider weighted multiple ergodic averages with weights coming from rational sets. I will give (easy to check) necessary and sufficient conditions for rational sets to be good for averaging (polynomial multiple) recurrence. If time permits, I will explain what role rational sets play in a structural decomposition of level sets of multiplicative functions.

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