On the logarithmic probability that a random integral ideal is A-free

Abstract

This extends a theorem of Davenport and Erdös (J Indian Math Soc 15:19–24, 1951) on sequences of rational integers to sequences of integral ideals in arbitrary number fields K. More precisely, we introduce a logarithmic density for sets of integral ideals in K and provide a formula for the logarithmic density of the set of so-called A -free ideals, i.e. integral ideals that are not multiples of any ideal from a fixed set A.