Prime numbers along Rudin–Shapiro sequences

For a large class of digital functions $f$, we estimate the sums $\sum_{n \leq x} \Lambda(n) f(n)$ (and $\sum_{n \leq x} \mu(n) f(n)$, where $\Lambda$ denotes the von Mangoldt function (and $\mu$ the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness pri...

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2015-01, Vol.17 (10), p.2595-2642
Hauptverfasser: Mauduit, Christian, Rivat, Joël
Format: Artikel
Sprache:eng
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Zusammenfassung:For a large class of digital functions $f$, we estimate the sums $\sum_{n \leq x} \Lambda(n) f(n)$ (and $\sum_{n \leq x} \mu(n) f(n)$, where $\Lambda$ denotes the von Mangoldt function (and $\mu$ 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.
ISSN:1435-9855
1435-9863
DOI:10.4171/JEMS/566