JournalsjemsVol. 17, No. 10pp. 2595–2642

Prime numbers along Rudin–Shapiro sequences

  • Christian Mauduit

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

    Université d'Aix-Marseille, Marseille, France
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Abstract

For a large class of digital functions ff, we estimate the sums nxΛ(n)f(n)\sum_{n \leq x} \Lambda(n) f(n) (and nxμ(n)f(n)\sum_{n \leq x} \mu(n) f(n), where Λ\Lambda denotes the von Mangoldt function (and μ\mu 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