Falko Baustian, Vladimir Bobkov
Published 2019-03-29Version 1
Let $f(n)$ be an arithmetic function with $f(1)\neq0$ and let $f^{-1}(n)$ be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behaviour of $|f^{-1}(n)|$ with regard to the asymptotic behaviour of $|f(n)|$ assuming that the latter one grows or decays with at most polynomial or exponential speed. As a by-product, we obtain simple but constructive upper bounds for the number of ordered factorizations of $n$ into $k$ factors.
Patterns in the iteration of an arithmetic function
Exponential and infinitary divisors
On the weighted average number of subgroups of ${\mathbb {Z}}_{m}\times {\mathbb {Z}}_{n}$ with $mn\leq x$
![QR code for arXiv:1903.12445 [math.NT]](http://oss.arxitics.com/images/favicon.svg)