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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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.

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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