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arXiv · 2401.16586

On counting totally imaginary number fields

A. Raghuram·Qiyao Yu
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Abstract

A number field is said to be a CM-number field if it is a totally imaginary quadratic extension of a totally real number field. We define a totally imaginary number field to be of CM-type if it contains a CM-subfield, and of TR-type if it does not contain a CM-subfield. For quartic totally imaginary number fields when ordered by discriminant, we show that about 69.95% are of TR-type and about 33.05% are of CM-type. For a sextic totally imaginary number field we classify its type in terms of its Galois group and possibly some additional information about the location of complex conjugation in the Galois group.

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A. Raghuram, Qiyao Yu. 2024-01-29. On counting totally imaginary number fields. https://arxiv.org/abs/2401.16586

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