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Independence of actions of (N,+) and (N,×) and Sarnak's Möbius disjointness conjecture

By Vitaly Bergelson

Appears in collection : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

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 Erdös-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,x). The talk is based on recent joint work with Florian Richter.

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Citation data

  • DOI 10.24350/CIRM.V.19686003
  • Cite this video Bergelson Vitaly (11/26/20). Independence of actions of (N,+) and (N,×) and Sarnak's Möbius disjointness conjecture. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19686003
  • URL https://dx.doi.org/10.24350/CIRM.V.19686003

Bibliography

  • BERGELSON, Vitaly et RICHTER, Florian K. Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions. arXiv preprint arXiv:2002.03498, 2020. - https://arxiv.org/abs/2002.03498

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