On the Riesz means of n/ϕ(n) - III
Ayyadurai Sankaranarayanan ; Saurabh Kumar Singh
Acta Arithmetica, Tome 168 (2015), p. 275-286 / Harvested from The Polish Digital Mathematics Library
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Let ϕ(n) denote the Euler totient function. We study the error term of the general kth Riesz mean of the arithmetical function n/ϕ(n) for any positive integer k ≥ 1, namely the error term Ek(x) where 1/k!∑n≤xn/ϕ(n)(1-n/x)k=Mk(x)+Ek(x). For instance, the upper bound for |Ek(x)| established here improves the earlier known upper bounds for all integers k satisfying k≫(logx)1+ϵ.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:279380 
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Ayyadurai Sankaranarayanan; Saurabh Kumar Singh. On the Riesz means of n/ϕ(n) - III. Acta Arithmetica, Tome 168 (2015) pp. 275-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-3-4/