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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Kandhil et al. (2024) studied this question.
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