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arXiv · 2402.13830

The Brauer-Siegel ratio for prime cyclotomic fields

Neelam Kandhil·Alessandro Languasco·Pieter Moree
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Abstract

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.

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Neelam Kandhil, Alessandro Languasco, Pieter Moree. 2024-02-21. The Brauer-Siegel ratio for prime cyclotomic fields. https://doi.org/10.2140/pjm.2025.334.16

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