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The Brauer–Siegel
ratio for prime cyclotomic fields
Neelam Kandhil, Alessandro Languasco and Pieter Moree |
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Vol. 334 (2025), No. 1, 167–182
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DOI: 10.2140/pjm.2025.334.167
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Abstract |
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The Brauer–Siegel theorem concerns the size of the product of the class number and the regulator of a number field . We derive bounds for this product in case 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. |
Keywords
cyclotomic fields, residues, class number, Siegel zero,
Dirichlet $L$-series
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Mathematical Subject Classification
Primary: 11R18, 11R29
Secondary: 11R47, 11Y60
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Milestones
Received: 19 March 2024
Revised: 7 January 2025
Accepted: 16 January 2025
Published: 31 January 2025
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Authors |
| Neelam Kandhil | |
| Department of Mathematics The University of Hong Kong Pokfulam Hong Kong |
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| Alessandro Languasco | |
| Department of Information
Engineering Università di Padova Padova Italy |
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| Pieter Moree | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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