On a sum involving the Möbius function

I. Kiuchi; M. Minamide; Y. Tanigawa

Acta Arithmetica, Tome 168 (2015), p. 149-168 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $c_{q} (n)$ be the Ramanujan sum, i.e. $c_{q} (n) = \sum_{d | (q, n)} d μ (q / d)$ , where μ is the Möbius function. In a paper of Chan and Kumchev (2012), asymptotic formulas for $\sum_{n \leq y} {(\sum_{q \leq x} c_{q} (n))}^{k}$ (k = 1,2) are obtained. As an analogous problem, we evaluate $\sum_{n \leq y} {(\sum_{n \leq x} c ̂_{q} (n))}^{k}$ (k = 1,2), where $c ̂_{q} (n) : = \sum_{d | (q, n)} d | μ (q / d) |$ .

Publié le : 2015-01-01

Zbl 1332.11088

EUDML-ID : urn:eudml:doc:278953

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     title = {On a sum involving the M\"obius function},
     journal = {Acta Arithmetica},
     volume = {168},
     year = {2015},
     pages = {149-168},
     zbl = {1332.11088},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-3}
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I. Kiuchi; M. Minamide; Y. Tanigawa. On a sum involving the Möbius function. Acta Arithmetica, Tome 168 (2015) pp. 149-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-3/