On a Mertens-type conjecture for number fields

Year: 2024

Type: article

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.

Source: Mathematical Proceedings of the Cambridge Philosophical Society

DOI: 10.1017/s0305004124000306

Authors: DANIEL HU, IKUYA KANEKO, SPENCER MARTIN, CARL SCHILDKRAUT

Institutions: Princeton University, California Institute of Technology, University of Virginia, Massachusetts Institute of Technology

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funders: National Science Foundation, University of Virginia, National Security Agency, Templeton World Charity Foundation

OpenAlex ID: W4405592065