00:00:00 / 00:00:00

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19686003
  • Cite this video Bergelson, Vitaly (26/11/2020). 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


  • 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

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow


  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
  • Get notification updates
    for your favorite subjects
Give feedback