On correlations of certain multiplicative functions

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• 作者：R. Balasubramanian^a ; ^b ; ^{balu@imsc.res.in} ; Sumit Giri^c ; ^{sumit.giri199@gmail.com} ; Priyamvad Srivastav^a ; ^b ; ^{priyamvads@imsc.res.in}
• 关键词：Asymptotic results on arithmetic functions ; Product of shifted multiplicative functions
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：174
• 期：Complete
• 页码：221-238
• 全文大小：321 K
• 卷排序：174

文摘

In this paper, we study sums of shifted products ∑n≤xF(n)G(n−h) for any |h|≤x/2|h|≤x/2 and arithmetic functions F=f⁎1F=f⁎1 and G=g⁎1G=g⁎1, with f and g small. We obtain asymptotic formula for different orders of magnitude of f and g  . We also provide asymptotic formula for sums of the type ∑n≤xμ2(n)G(n−h), where G=g⁎1G=g⁎1 and g is small. For small order of magnitudes of f and g, we improve the error terms and make them independent of h.