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Ergodicity of the Liouville system implies the Chowla conjecture

By Nikos Frantzikinakis

Appears in collections : 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, Exposés de recherche

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.

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Citation data

  • DOI 10.24350/CIRM.V.19101103
  • Cite this video Frantzikinakis, Nikos (12/12/2016). Ergodicity of the Liouville system implies the Chowla conjecture. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19101103
  • URL https://dx.doi.org/10.24350/CIRM.V.19101103

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