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An asymptotic formula related to the sums of divisors

Volume 175 / 2016

Meng Zhang Acta Arithmetica 175 (2016), 183-200 MSC: 11N37, 11P55, 11L03. DOI: 10.4064/aa8391-5-2016 Published online: 19 September 2016

Abstract

Let $d(n)$ be the number of divisors of $n$, and $k$ a positive integer. It is proved that the sum $\sum_{1\leq m_1,\dots,m_s\leq X}d(m_1^k+\cdots+m_s^k)$ has an asymptotic formula for $k\geq2$ and $s \gt \min\{2^{k-1}, k^2+k-2\}.$

Authors

  • Meng ZhangSchool of Mathematics and Quantitative Economics
    Shandong University of Finance and Economics
    40 Shungeng Road
    Jinan, Shandong 250014, P.R. China
    e-mail

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