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 |
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Hauptverfasser: | , |
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. |
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ISSN: | 1435-9855 1435-9863 |
DOI: | 10.4171/JEMS/566 |