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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2309.03745 |
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| _version_ | 1866909116322021376 |
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| author | Bhattacharyya, Arindam Kadiri, Vishnu Ray, Anwesh |
| author_facet | Bhattacharyya, Arindam Kadiri, Vishnu Ray, Anwesh |
| contents | Let $p$ be an odd prime number. We study growth patterns associated with finitely ramified Galois groups considered over the various number fields varying in a $\mathbb{Z}_p$-tower. These Galois groups can be considered as non-commutative analogues of ray class groups. For certain $\mathbb{Z}_p$-extensions in which a given prime above $p$ is completely split, we prove precise asymptotic lower bounds. Our investigations are motivated by the classical results of Iwasawa, who showed that there are growth patterns for $p$-primary class numbers of the number fields in a $\mathbb{Z}_p$-tower. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03745 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic growth patterns for class field towers Bhattacharyya, Arindam Kadiri, Vishnu Ray, Anwesh Number Theory 11R23 Let $p$ be an odd prime number. We study growth patterns associated with finitely ramified Galois groups considered over the various number fields varying in a $\mathbb{Z}_p$-tower. These Galois groups can be considered as non-commutative analogues of ray class groups. For certain $\mathbb{Z}_p$-extensions in which a given prime above $p$ is completely split, we prove precise asymptotic lower bounds. Our investigations are motivated by the classical results of Iwasawa, who showed that there are growth patterns for $p$-primary class numbers of the number fields in a $\mathbb{Z}_p$-tower. |
| title | Asymptotic growth patterns for class field towers |
| topic | Number Theory 11R23 |
| url | https://arxiv.org/abs/2309.03745 |