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An additive divisor problem with a growing number of factors
N. M. Timofeev
Vladimir State Pedagogical University
Abstract:
Let $\tau_k(n)$ be the number of representations of $n$ as the product of $k$ positive factors, $\tau_2(n)=\tau(n)$. The asymptotics of $\sum_{n\le x}\tau_k(n)\tau(n+1)$ for $80k^{10}(\ln\ln x)^3\le\ln x$ is shown to be uniform with respect to $k$.
DOI:
https://doi.org/10.4213/mzm1513
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English version:
Mathematical Notes, 1997, 61:3, 321–332
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UDC:
511
Received: 15.11.1995
Citation:
N. M. Timofeev, “An additive divisor problem with a growing number of factors”, Mat. Zametki, 61:3 (1997), 391–406; Math. Notes, 61:3 (1997), 321–332
Citation in format AMSBIB
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\jour Math. Notes
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\vol 61
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\pages 321--332
\crossref{https://doi.org/10.1007/BF02355414}
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