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. 2595–2642DOI 10.4171/JEMS/566