Geodesic
Prime numbers along Rudin–Shapiro sequences
Journal of the European Mathematical Society, Tome 17 (2015) no. 10, pp. 2595-2642 Cet article a éte moissonné depuis la source EMS Press

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For a large class of digital functions f, we estimate the sums ∑n≤x​Λ(n)f(n) (and ∑n≤x​μ(n)f(n), where Λ denotes the von Mangoldt function (and μ 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.
DOI : 10.4171/jems/566
Classification : 11-XX
Keywords: Rudin–Shapiro sequence, prime numbers, Möbius function, exponential sums 
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     author = {Christian Mauduit and Jo\"el Rivat},
     title = {Prime numbers along {Rudin{\textendash}Shapiro} sequences},
     journal = {Journal of the European Mathematical Society},
     pages = {2595--2642},
     year = {2015},
     volume = {17},
     number = {10},
     doi = {10.4171/jems/566},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/566/}
}
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Christian Mauduit; Joël Rivat. Prime numbers along Rudin–Shapiro sequences. Journal of the European Mathematical Society, Tome 17 (2015) no. 10, pp. 2595-2642. doi: 10.4171/jems/566

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