Bi-quadratic Pólya fields with five distinct ramified primes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910561637236736 |
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| author | Islam, Md. Imdadul Chattopadhyay, Jaitra Chakraborty, Debopam |
| author_facet | Islam, Md. Imdadul Chattopadhyay, Jaitra Chakraborty, Debopam |
| contents | For an algebraic number field $K$, the Pólya group of $K$, denoted by $Po(K),$ is the subgroup of the ideal class group $Cl_{K}$ generated by the ideal classes of the products of prime ideals of same norm. The number field $K$ is said to be Pólya if $Po(K)$ is trivial. Motivated by several recent studies on the group $Po(K)$ when $K$ is a totally real bi-quadratic field, we investigate the same with five distinct odd primes ramifying in $K/\mathbb{Q}$. This extends the previous results on this problem, where the number of distinct ramified primes was at most four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bi-quadratic Pólya fields with five distinct ramified primes Islam, Md. Imdadul Chattopadhyay, Jaitra Chakraborty, Debopam Number Theory For an algebraic number field $K$, the Pólya group of $K$, denoted by $Po(K),$ is the subgroup of the ideal class group $Cl_{K}$ generated by the ideal classes of the products of prime ideals of same norm. The number field $K$ is said to be Pólya if $Po(K)$ is trivial. Motivated by several recent studies on the group $Po(K)$ when $K$ is a totally real bi-quadratic field, we investigate the same with five distinct odd primes ramifying in $K/\mathbb{Q}$. This extends the previous results on this problem, where the number of distinct ramified primes was at most four. |
| title | Bi-quadratic Pólya fields with five distinct ramified primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.05157 |