The Kummer ratio of the relative class number for prime cyclotomic fields
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910815722930176 |
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| author | Kandhil, Neelam Languasco, Alessandro Moree, Pieter Eddin, Sumaia Saad Sedunova, Alisa |
| author_facet | Kandhil, Neelam Languasco, Alessandro Moree, Pieter Eddin, Sumaia Saad Sedunova, Alisa |
| contents | Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three scenarios: no Siegel zero, presence of Siegel zero and assuming the Riemann Hypothesis for the Dirichlet $L$-series attached to odd characters only. The numerical work in this paper extends and improves on our earlier preprint (arXiv:1908.01152) and demonstrates our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Kummer ratio of the relative class number for prime cyclotomic fields Kandhil, Neelam Languasco, Alessandro Moree, Pieter Eddin, Sumaia Saad Sedunova, Alisa Number Theory Primary 11R18, 11R29, Secondary 11R47, 11Y60 Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three scenarios: no Siegel zero, presence of Siegel zero and assuming the Riemann Hypothesis for the Dirichlet $L$-series attached to odd characters only. The numerical work in this paper extends and improves on our earlier preprint (arXiv:1908.01152) and demonstrates our theoretical results. |
| title | The Kummer ratio of the relative class number for prime cyclotomic fields |
| topic | Number Theory Primary 11R18, 11R29, Secondary 11R47, 11Y60 |
| url | https://arxiv.org/abs/2402.13829 |