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Sectio Computatorica

Volumes » Volume 54 (2023)

https://doi.org/10.71352/ac.54.295

The ring of arithmetical functions in the rational domain

Vilius Stakėnas

Abstract. The arithmetical functions with rational argument are interpreted as sums of weighted divisors: $$ f(r)=\sum_{d|r}w(d). $$ The logarithmic density of subsets of rational numbers is introduced. It is proved, that if \( w(d)\geqslant 0\), then asymptotic logarithmic density of the set \(\{r: f(r)\geqslant z\}\) exists.

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