%0 Journal Article
%T Sets with prescribed arithmetic densities
%A Florian Luca
%A Carl Pomerance
%A £¿tefan Porubsky
%J Uniform Distribution Theory
%D 2008
%I Mathematical Institute of the Slovak Academy of Sciences
%X Using concepts of generalized asymptotic and logarithmic densities based on weighted arithmetic means over an arithmetical semigroup $\mathbb{G}$ we prove that under some additional technical assumptions on the weighted counting function of its elements, a subset of $\mathbb{G}$ exists with all four generalized densities (upper and lower asymptotic and logarithmic) prescribed subject to the natural condition $0 \leq \underline{d}(A) \leq \underline{\ell}(A) \leq \overline{\ell}(A) \leq \overline{d}(A) \leq1$.
%K Generalized arithmetic density
%K generalized asymptotic density
%K generalized logarithmic density
%K arithmetical semigroup
%K weighted arithmetic mean
%K ratio set
%K $R$-dense set
%K Axiom A
%K $\
%K delta$-regularly varying function
%U http://www.boku.ac.at/MATH/udt/vol03/no2/LuPoPor08-2.pdf