Geodesic
Ergodicity of the Liouville system implies the Chowla conjecture
Discrete analysis (2017)

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arXiv
The Chowla conjecture asserts that the values of the Liouville function form a normal sequence of plus and minus ones. Reinterpreted in the language of ergodic theory it asserts that the Liouville function is generic for the Bernoulli measure on the space of sequences with values plus or minus one. We show that these statements are implied by the much weaker hypothesis that the Liouville function is generic for an ergodic measure. We also give variants of this result related to a conjecture of Elliott on correlations of multiplicative functions with values on the unit circle. Our argument has an ergodic flavor and combines recent results in analytic number theory, finitistic and infinitary decomposition results involving uniformity seminorms, and qualitative equidistribution results on nilmanifolds.
Publié le : 
Nikos Frantzikinakis. Ergodicity of the Liouville system implies the Chowla conjecture. Discrete analysis (2017). http://geodesic.mathdoc.fr/item/DAS_2017_a1/
@article{DAS_2017_a1,
     author = {Nikos Frantzikinakis},
     title = {Ergodicity of the {Liouville} system implies the {Chowla} conjecture},
     journal = {Discrete analysis},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2017_a1/}
}
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JO  - Discrete analysis
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