Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions

Olivier Ramaré. "Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions." Acta Arithmetica 165.1 (2014): 1-10. <http://eudml.org/doc/279409>.

@article{OlivierRamaré2014,
abstract = {We prove that $|∑_\{d≤x,(d,q)=1\} μ(d)/d| ≤ 2.4(q/φ(q))/log(x/q)$ for every x > q ≥ 1, and similar estimates for the Liouville function. We also give better constants when x/q is large.,},
author = {Olivier Ramaré},
journal = {Acta Arithmetica},
keywords = {Möbius function; Liouville function; explicit estimates},
language = {eng},
number = {1},
pages = {1-10},
title = {Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions},
url = {http://eudml.org/doc/279409},
volume = {165},
year = {2014},
}

TY - JOUR
AU - Olivier Ramaré
TI - Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 1
SP - 1
EP - 10
AB - We prove that $|∑_{d≤x,(d,q)=1} μ(d)/d| ≤ 2.4(q/φ(q))/log(x/q)$ for every x > q ≥ 1, and similar estimates for the Liouville function. We also give better constants when x/q is large.,
LA - eng
KW - Möbius function; Liouville function; explicit estimates
UR - http://eudml.org/doc/279409
ER -