On a Mertens-type conjecture for number fields
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 generalised Mertens function of certain dicyclic number fields as consequences of Artin factorisation.
Authors
- Daniel Hu (ORCID: https://orcid.org/0000-0002-9942-7463)
- Ikuya Kaneko (ORCID: https://orcid.org/0000-0003-4518-1805)
- Carl Schildkraut
- Spencer Martin
Institutions
- California Institute of Technology (US)
- Princeton University (US)
- University of Virginia (US)
- Massachusetts Institute of Technology (US)
Publication Details
- Journal
- Mathematical Proceedings of the Cambridge Philosophical Society
- Published
- 2024-11-01
- DOI
- https://doi.org/10.1017/s0305004124000306
- Citations
- 1
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 1.27
Funders
- National Science Foundation
- University of Virginia
- National Security Agency
- Templeton World Charity Foundation