The Brauer-Siegel ratio for prime cyclotomic fields
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913673482600448 |
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| author | Kandhil, Neelam Languasco, Alessandro Moree, Pieter |
| author_facet | Kandhil, Neelam Languasco, Alessandro Moree, Pieter |
| contents | The Brauer-Siegel theorem concerns the size of the product of the class number and the regulator of a number field $K$. We derive bounds for this product in case $K$ is a prime cyclotomic field, distinguishing between whether there is a Siegel zero or not. In particular, we make a result of Tatuzawa (1953) more explicit. Our theoretical advancements are complemented by numerical illustrations that are consistent with our findings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_13830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Brauer-Siegel ratio for prime cyclotomic fields Kandhil, Neelam Languasco, Alessandro Moree, Pieter Number Theory Primary 11R18, 11R29, Secondary 11R47, 11Y60 The Brauer-Siegel theorem concerns the size of the product of the class number and the regulator of a number field $K$. We derive bounds for this product in case $K$ is a prime cyclotomic field, distinguishing between whether there is a Siegel zero or not. In particular, we make a result of Tatuzawa (1953) more explicit. Our theoretical advancements are complemented by numerical illustrations that are consistent with our findings. |
| title | The Brauer-Siegel ratio for prime cyclotomic fields |
| topic | Number Theory Primary 11R18, 11R29, Secondary 11R47, 11Y60 |
| url | https://arxiv.org/abs/2402.13830 |