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

Volume 165 / 2014

Olivier Ramaré Acta Arithmetica 165 (2014), 1-10 MSC: Primary 11N37, 11Y35; Secondary 11A25. DOI: 10.4064/aa165-1-1


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.,


  • Olivier RamaréCNRS, Laboratoire Paul Painlevé
    Université Lille 1
    59 655 Villeneuve d'Ascq, France

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