Prime numbers along Rudin–Shapiro sequences
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 …