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arXiv · 1806.01404

Note on the number of divisors of reducible quadratic polynomials

Adrian W. Dudek·Łukasz Pańkowski·Victor Scharaschkin
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Abstract

In a recent paper, Lapkova uses a Tauberian theorem to derive the asymptotic formula for the divisor sum $\sum_{n \leq x} d( n (n+v))$ where $v$ is a fixed integer and $d(n)$ denotes the number of divisors of $n$. We reprove her result by following a suggestion of Hooley, namely investigating the relationship between this sum and the well-known sum $\sum_{n \leq x} d( n ) d (n+v)$. As such, we are able to furnish additional terms in the asymptotic formula.

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Adrian W. Dudek, Łukasz Pańkowski, Victor Scharaschkin. 2018-06-04. Note on the number of divisors of reducible quadratic polynomials. https://doi.org/10.1017/s0004972718000734

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