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- Title
NOTE ON THE NUMBER OF DIVISORS OF REDUCIBLE QUADRATIC POLYNOMIALS.
- Authors
DUDEK, ADRIAN W.; PAŃKOWSKI, ŁUKASZ; SCHARASCHKIN, VICTOR
- Abstract
Lapkova ['On the average number of divisors of reducible quadratic polynomials', J. Number Theory 180 (2017), 710–729] uses a Tauberian theorem to derive an 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 this result with additional terms in the asymptotic formula, by investigating the relationship between this divisor sum and the well-known sum $\sum _{n\leq x}d(n)d(n+v)$.
- Subjects
SMALL divisors; POLYNOMIALS; INTEGERS; TAUBERIAN theorems; NUMBER theory
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p1
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718000734