An Improved Asymptotic on the Representations of Integers as Sums of Products

Wenjia Zhao and Jie Wu

Journal of Mathematics, 2021, vol. 2021, 1-11

Abstract: In this paper, we improve the error terms of Chace’s results in the study by Chace (1994) on the number of ways of writing an integer N as a sum of k products of l factors, valid for k≥3 and l=2, 3. More precisely, for l=2, 3, we improve the upper bound Nk−1−2k−2/k−1l+1+ε, k≥3 for the error term, to N2−2/2l+1+ε when k=3 and Nk−1−4k−2/l+1k+l−2+ε when k≥4.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2902015

DOI: 10.1155/2021/2902015

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