Prime numbers along Rudin–Shapiro sequences

Mauduit, Christian, and Rivat, Joël. "Prime numbers along Rudin–Shapiro sequences." Journal of the European Mathematical Society 017.10 (2015): 2595-2642. <http://eudml.org/doc/277387>.

@article{Mauduit2015,
abstract = {For a large class of digital functions $f$, we estimate the sums $\sum _\{n \le x\} \Lambda (n) f(n)$ (and $\sum _\{n \le x\} \mu (n) f(n)$, 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.},
author = {Mauduit, Christian, Rivat, Joël},
journal = {Journal of the European Mathematical Society},
keywords = {Rudin–Shapiro sequence; prime numbers; Möbius function; exponential sums; Rudin-Shapiro sequence; prime numbers; Möbius function; exponential sums},
language = {eng},
number = {10},
pages = {2595-2642},
publisher = {European Mathematical Society Publishing House},
title = {Prime numbers along Rudin–Shapiro sequences},
url = {http://eudml.org/doc/277387},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Mauduit, Christian
AU - Rivat, Joël
TI - Prime numbers along Rudin–Shapiro sequences
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 10
SP - 2595
EP - 2642
AB - For a large class of digital functions $f$, we estimate the sums $\sum _{n \le x} \Lambda (n) f(n)$ (and $\sum _{n \le x} \mu (n) f(n)$, 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.
LA - eng
KW - Rudin–Shapiro sequence; prime numbers; Möbius function; exponential sums; Rudin-Shapiro sequence; prime numbers; Möbius function; exponential sums
UR - http://eudml.org/doc/277387
ER -