Prime numbers along Rudin–Shapiro sequences

  • Christian Mauduit

    Université d'Aix-Marseille, Marseille, France
  • Joël Rivat

    Université d'Aix-Marseille, Marseille, France


For a large class of digital functions , we estimate the sums (and , where denotes the von Mangoldt function (and the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.

Cite this article

Christian Mauduit, Joël Rivat, Prime numbers along Rudin–Shapiro sequences. J. Eur. Math. Soc. 17 (2015), no. 10, pp. 2595–2642

DOI 10.4171/JEMS/566