ON SARNAK'S CONJECTURE AND VEECH'S QUESTION FOR INTERVAL EXCHANGES

Sébastien Ferenczi (1) , Christian Mauduit (2)

1 IML - Institut de mathématiques de Luminy
2 I2M - Institut de Mathématiques de Marseille

Using a criterion due to Bourgain [10] and the generalization of the self-dual induction defined in [18], 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.

Domaines: Mathématiques [math]

Sébastien Ferenczi, Christian Mauduit. ON SARNAK'S CONJECTURE AND VEECH'S QUESTION FOR INTERVAL EXCHANGES. Journal d'analyse mathématique, 2018, 134. ⟨hal-01263088⟩