On a Mertens-type conjecture for number fields
Number Theory
2025-01-15 v2
Abstract
We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence of a logarithmic limiting distribution for the analogous Mertens function, expanding upon work of Ng. Finally, we explore properties of the generalized Mertens function of certain dicyclic number fields as consequences of Artin factorization.
Cite
@article{arxiv.2109.06665,
title = {On a Mertens-type conjecture for number fields},
author = {Daniel Hu and Ikuya Kaneko and Spencer Martin and Carl Schildkraut},
journal= {arXiv preprint arXiv:2109.06665},
year = {2025}
}
Comments
37 pages, 4 tables