Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions
Acta Arithmetica, Tome 165 (2014) no. 1, pp. 1-10
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that
$|\!\sum_{d\le x,\, (d,q)=1}\mu(d)/d|\le 2.4(q/\varphi(q))/\!\log
(x/q)$ for every $x>q\ge1$, and similar estimates for the Liouville
function. We also give better constants when $x/q$ is large.,
Keywords:
prove sum varphi log every similar estimates liouville function better constants large
Affiliations des auteurs :
Olivier Ramaré 1
@article{10_4064_aa165_1_1,
author = {Olivier Ramar\'e},
title = {Explicit estimates on the summatory functions of the {M\"obius} function with coprimality restrictions},
journal = {Acta Arithmetica},
pages = {1--10},
publisher = {mathdoc},
volume = {165},
number = {1},
year = {2014},
doi = {10.4064/aa165-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa165-1-1/}
}
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Olivier Ramaré. Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions. Acta Arithmetica, Tome 165 (2014) no. 1, pp. 1-10. doi: 10.4064/aa165-1-1
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