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On Sarnak’s conjecture and Veech’s question for interval exchanges

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Abstract

Using a criterion due to Bourgain [10] and the generalization of the self-dual induction defined in [19], for each primitive permutation we build a large family of k-interval exchanges satisfying Sarnak’s conjecture, and, for at least one permutation in each Rauzy class, smaller families for which we have weak mixing, which implies a prime number theorem, and simplicity in the sense of Veech.

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Authors and Affiliations

  1. Institut de Mathématiques de Marseille, CNRS - UMR 7373, Case 907 - 163 av. de Luminy, F13288, Marseille Cedex 9, France

    Sébastien Ferenczi & Christian Mauduit

Authors
  1. Sébastien Ferenczi
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  2. Christian Mauduit
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Corresponding author

Correspondence to Sébastien Ferenczi.

Additional information

Most of this research was carried out while the first author was in Unité Mixte IMPA-CNRS in Rio de Janeiro and the second author was a temporary visitor of IMPA.

The first author was also partially supported by the ANR GeoDyn and the ANR DYna3S.

The second author was supported by the ANR MUNUM, Réseau Franco-Brésilien en Mathématiques (Proc. CNPq 60-0014/01-5 and 69-0140/03-7), Math Am Sud program DYSTIL, BREUDS (IRSES GA318999) and Ciência sem Fronteiras (PVE 407308/2013-0)

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Ferenczi, S., Mauduit, C. On Sarnak’s conjecture and Veech’s question for interval exchanges. JAMA 134, 545–573 (2018). https://doi.org/10.1007/s11854-018-0017-z

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  • DOI: https://doi.org/10.1007/s11854-018-0017-z

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