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A dynamical approach to the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions

Vitaly Bergelson (Ohio State and IAS)

Location:  Hill Center Room 705
Date & time: Wednesday, 01 February 2023 at 3:30PM - 4:30PM

Abstract: We will discuss a new type of ergodic theorem which has among its corollaries numerous classical results from multiplicative number theory, including the Prime Number Theorem, a theorem of Pillai-Selberg and a theorem of Erd?s-Delange. This ergodic approach leads to a new dynamical framework for a general form of Sarnak’s Möbius disjointness conjecture which focuses on the "joint independence" of actions of (N,+) and (N,×). The talk is based on recent joint work with Florian Richter.