On Iwasawa's class number formula for $\mathbb{Z}_p\rtimes\mathbb{Z}_p$-extensions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2017
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| Acceso en línea: | |
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| _version_ | 1866929199991750656 |
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| author | Tateno, Sohei |
| author_facet | Tateno, Sohei |
| contents | Let $p$ be a prime number. In this paper, we estimate the variation of the sizes of quotients of certain finitely generated $p$-torsion Iwasawa modules, which are closely related to class numbers. We also construct some $\mathbb{Z}_p\rtimes\mathbb{Z}_p$-extensions whose Iwasawa $μ$-invariant is nonzero. At the end of this paper, we calculate the determinants of some matrices that are related to the groups $\mathbb{Z}_p\rtimes\mathbb{Z}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_10966 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On Iwasawa's class number formula for $\mathbb{Z}_p\rtimes\mathbb{Z}_p$-extensions Tateno, Sohei Number Theory Let $p$ be a prime number. In this paper, we estimate the variation of the sizes of quotients of certain finitely generated $p$-torsion Iwasawa modules, which are closely related to class numbers. We also construct some $\mathbb{Z}_p\rtimes\mathbb{Z}_p$-extensions whose Iwasawa $μ$-invariant is nonzero. At the end of this paper, we calculate the determinants of some matrices that are related to the groups $\mathbb{Z}_p\rtimes\mathbb{Z}_p$. |
| title | On Iwasawa's class number formula for $\mathbb{Z}_p\rtimes\mathbb{Z}_p$-extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/1710.10966 |