On counting totally imaginary number fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910311109361664 |
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| author | Raghuram, A. Yu, Qiyao |
| author_facet | Raghuram, A. Yu, Qiyao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On counting totally imaginary number fields Raghuram, A. Yu, Qiyao Number Theory 11R45, 11R16, 11R21, 11R32 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. |
| title | On counting totally imaginary number fields |
| topic | Number Theory 11R45, 11R16, 11R21, 11R32 |
| url | https://arxiv.org/abs/2401.16586 |