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On the asymptotic behavior of sums ∑n≤xf(n){x/n}k
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2019-12-26 , DOI: 10.1142/s1793042120500657
Liuying Wu 1 , Sanying Shi 1
Affiliation  

Let [Formula: see text] be an arbitrary real-valued positive nondecreasing function, in this paper we prove that [Formula: see text] [Formula: see text] where [Formula: see text] is the sum given in the title, [Formula: see text] and [Formula: see text] is a positive integer. This improves the result of Mercier and Nowak.

中文翻译:

关于和∑n≤xf(n){x/n}k的渐近行为

令[Formula: see text]为任意实值正非减函数,本文证明[Formula: see text] [Formula: see text] 其中[Formula: see text]是标题中给出的和, [公式:见正文]和[公式:见正文]为正整数。这改善了 Mercier 和 Nowak 的结果。
更新日期:2019-12-26
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