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Transactions of the American Mathematical Society

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Asymptotic estimates of sums involving the Moebius function. II

Author: Krishnaswami Alladi
Journal: Trans. Amer. Math. Soc. 272 (1982), 87-105
MSC: Primary 10H15; Secondary 10H25
MathSciNet review: 656482
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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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Keywords: Moebius function, asymptotic estimate, largest and smallest prime factors
Article copyright: © Copyright 1982 American Mathematical Society

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