The Brauer-Siegel ratio for prime cyclotomic fields
Number Theory
2025-02-04 v2
Abstract
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
Cite
@article{arxiv.2402.13830,
title = {The Brauer-Siegel ratio for prime cyclotomic fields},
author = {Neelam Kandhil and Alessandro Languasco and Pieter Moree},
journal= {arXiv preprint arXiv:2402.13830},
year = {2025}
}
Comments
16 pages, 3 figures. Rewritten and improved section 3; updated references