Pólya-Ostrowski Group and Unit Index in Real Biquadratic Fields
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914225321934848 |
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| author | Al-Jabbari, Huda Naeem Hleeb Maarefparvar, Abbas |
| author_facet | Al-Jabbari, Huda Naeem Hleeb Maarefparvar, Abbas |
| contents | The Pólya-Ostrowski group of a Galois number field $K$, is the subgroup $Po(K)$ of the ideal class group $Cl(K)$ of $K$ generated by the classes of all the strongly ambiguous ideals of $K$. The number field $K$ is called a Pólya field, whenever $Po(K)$ is trivial. In this paper, using some results of Bennett Setzer \cite{Bennett} and Zantema \cite{Zantema}, we give an explicit relation between the order of Pólya groups and the Hasse unit indices in real biquadratic fields. As an application, we refine Zantema's upper bound on the number of ramified primes in Pólya real biquadratic fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_01904 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Pólya-Ostrowski Group and Unit Index in Real Biquadratic Fields Al-Jabbari, Huda Naeem Hleeb Maarefparvar, Abbas Number Theory 11R11, 11R16, 11R27, 11R34 The Pólya-Ostrowski group of a Galois number field $K$, is the subgroup $Po(K)$ of the ideal class group $Cl(K)$ of $K$ generated by the classes of all the strongly ambiguous ideals of $K$. The number field $K$ is called a Pólya field, whenever $Po(K)$ is trivial. In this paper, using some results of Bennett Setzer \cite{Bennett} and Zantema \cite{Zantema}, we give an explicit relation between the order of Pólya groups and the Hasse unit indices in real biquadratic fields. As an application, we refine Zantema's upper bound on the number of ramified primes in Pólya real biquadratic fields. |
| title | Pólya-Ostrowski Group and Unit Index in Real Biquadratic Fields |
| topic | Number Theory 11R11, 11R16, 11R27, 11R34 |
| url | https://arxiv.org/abs/2108.01904 |