Asymptotic estimates of sums involving the Moebius function |
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Authors: | Krishnaswami Alladi |
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Institution: | Department of Mathematics, University of Michigan Ann Arbor, Michigan 48109 USA |
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Abstract: | Let p(n) denote the smallest prime factor of an integer n>1 and let p(1)=∞. We study the asymptotic behavior of the sum M(x,y)=Σ1≤n≤x,p(n)>yμ(n) and use this to estimate the size of A(x)=max|f|≤1|Σ2≤n<xμ(n)f(p(n))|, where μ(n) is the Moebius function. Applications of bounds for A(x), M(x,y) and similar quantities are discussed. |
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