Class numbers of Imaginary bicyclic biquadratic number fields
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908542753046528 |
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| author | Jakhar, Anuj Kalwaniya, Ravi Ram, Mahesh Kumar |
| author_facet | Jakhar, Anuj Kalwaniya, Ravi Ram, Mahesh Kumar |
| contents | For any fixed positive integer $n$, we provide a method to compute all imaginary bicyclic biquadratic number fields with class number $n$, along with their class group structures, using the list of all imaginary quadratic number fields whose class numbers divide $2n$. We apply this method to list all imaginary bicyclic biquadratic number fields with class numbers $4$, $6$ and $7$. We also present the class group structure of each subfield of these fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Class numbers of Imaginary bicyclic biquadratic number fields Jakhar, Anuj Kalwaniya, Ravi Ram, Mahesh Kumar Number Theory 11R11, 11R29 For any fixed positive integer $n$, we provide a method to compute all imaginary bicyclic biquadratic number fields with class number $n$, along with their class group structures, using the list of all imaginary quadratic number fields whose class numbers divide $2n$. We apply this method to list all imaginary bicyclic biquadratic number fields with class numbers $4$, $6$ and $7$. We also present the class group structure of each subfield of these fields. |
| title | Class numbers of Imaginary bicyclic biquadratic number fields |
| topic | Number Theory 11R11, 11R29 |
| url | https://arxiv.org/abs/2509.13153 |