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Volume 178 / 2017

Gautier Hanna Acta Arithmetica 178 (2017), 15-42 MSC: Primary 11A63; Secondary 11B85, 11N05, 11L20. DOI: 10.4064/aa8337-8-2016 Published online: 5 January 2017

Abstract

We generalize Mauduit and Rivat’s theorem on the Rudin–Shapiro sequence. Weakening the hypothesis needed in their theorem, we prove a prime number theorem for a large class of functions defined on the digits. Our result covers the case of generalized Rudin–Shapiro sequences as well as block-additive sequences on finite and infinite expansions. We also give a partial answer to a question posed by Kalai.

Authors

  • Gautier HannaUniversité de Lorraine et CNRS
    Institut Élie Cartan de Lorraine, UMR 7502
    F-54506 Vandœuvre-lès-Nancy, France
    e-mail

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