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On a Mertens-type conjecture for number fields. (arXiv:2109.06665v2 [math.NT] UPDATED)

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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.

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