# Prime numbers along Rudin–Shapiro sequences

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 10, page 2595-2642
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topMauduit, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.