Journal
JOURNAL OF NUMBER THEORY
Volume 247, Issue -, Pages 35-45Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jnt.2022.12.004
Keywords
Asymptotic formula; Multiple exponential sums; Mobius transformation; Integral part function
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This paper studies a small arithmetic function and its sum as x approaches infinity, which generalizes previous works and combines different types of sums.
Let f be a small arithmetic function in the sense that f = g *1 and g(n) << n-j, where j is a fixed non-negative number. In this paper, we study the sum Sigma(n <= x) f([x/n])/[x/n](k) as x -> infinity, where [center dot] denotes the integral part function and k is a fixed non-negative number. Our results generalize the very recent work of Stucky, also combine and generalize the original two types of sums studied by Bordelles-Dai-Heyman-Pan-Shparlinski. (c) 2023 Elsevier Inc. All rights reserved.
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