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Ergodicity of the Liouville system implies the Chowla conjecture

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Authors : Frantzikinakis, Nikos (Author of the conference)
CIRM (Publisher )

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Abstract : The Chowla conjecture asserts that the signs of the Liouville function are distributed randomly on the integers. Reinterpreted in the language of ergodic theory this conjecture asserts that the Liouville dynamical system is a Bernoulli system. We prove that ergodicity of the Liouville system implies the Chowla conjecture. Our argument has an ergodic flavor and combines recent results in analytic number theory, finitistic and infinitary decomposition results involving uniformity norms, and equidistribution results on nilmanifolds.

MSC Codes :
11N37 - Asymptotic results on arithmetic functions
11N60 - Distribution functions (additive and positive multiplicative functions)
37A45 - Relations of ergodic theory with number theory and harmonic analysis
11B30 - Arithmetic combinatorics; higher degree uniformity

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 06/01/17
    Conference Date : 12/12/16
    Subseries : Research talks
    arXiv category : Dynamical Systems ; Number Theory
    Mathematical Area(s) : Dynamical Systems & ODE ; Number Theory
    Format : MP4 (.mp4) - HD
    Video Time : 01:00:08
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2016-12-12_Frantzikinakis.mp4

Information on the Event

Event Title : Jean-Morlet Chair: Ergodic theory and its connections with arithmetic and combinatorics / Chaire Jean Morlet : Théorie ergodique et ses connexions avec l'arithmétique et la combinatoire
Event Organizers : Cassaigne, Julien ; Ferenczi, Sébastien ; Hubert, Pascal ; Kulaga-Przymus, Joanna ; Lemanczyk, Mariusz
Dates : 12/12/16 - 16/12/16
Event Year : 2016
Event URL : https://www.chairejeanmorlet.com/1553.html

Citation Data

DOI : 10.24350/CIRM.V.19101103
Cite this video as: Frantzikinakis, Nikos (2016). Ergodicity of the Liouville system implies the Chowla conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19101103
URI : http://dx.doi.org/10.24350/CIRM.V.19101103

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