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 $k$.

UDC: 511

Received: 15.11.1995

DOI: 10.4213/mzm1513

 English version: Mathematical Notes, 1997, 61:3, 321–332

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