On the logarithmic probability that a random integral ideal is $\mathscr A$-free
Number Theory
2018-08-30 v1
Abstract
This extends a theorem of Davenport and Erd\"os on sequences of rational integers to sequences of integral ideals in arbitrary number fields . More precisely, we introduce a logarithmic density for sets of integral ideals in and provide a formula for the logarithmic density of the set of so-called -free ideals, i.e. integral ideals that are not multiples of any ideal from a fixed set .
Cite
@article{arxiv.1712.03015,
title = {On the logarithmic probability that a random integral ideal is $\mathscr A$-free},
author = {Christian Huck},
journal= {arXiv preprint arXiv:1712.03015},
year = {2018}
}
Comments
9 pages, to appear in S. Ferenczi, J. Ku{\l}aga-Przymus and M. Lema\'nczyk (eds.), Chowla's conjecture: from the Liouville function to the M\"obius function, Lecture Notes in Math., Springer