Asymptotic estimates of sums involving the Moebius function. II

Alladi, Krishnaswami

doi:10.1090/S0002-9947-1982-0656482-7

Asymptotic estimates of sums involving the Moebius function. II
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Trans. Amer. Math. Soc. 272 (1982), 87-105 Request permission

Abstract:

Let $n$ be a positive integer and $\mu (n)$ the Moebius function. If $n > 1$, let $P(n)$ denote its largest prime factor and put $P(1) = 1$. We study the asymptotic behavior of the sum ${M^ \ast }(x,y) = \sum \nolimits _{1 \leqslant n \leqslant x,P(n) < y} {\mu (n)}$ as $x,y \to \infty$ and discuss a few applications.

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