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arXiv · 2609.05950

On the class number of certain cyclotomic fields

Kalyan Chakraborty·Pratik Rao
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Abstract

We construct four infinite families of cyclotomic fields and show that each member of these families has class number a multiple of 3. In fact, we show that the class number of the corresponding maximal real subfields has class number divisible by 3. A construction by Kishi and Miyake [11] and a result of Yamaguchi [13] help us achieve this target. Finally, we produce computational evidence corroborating our results.

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Kalyan Chakraborty, Pratik Rao. 2026-09-05. On the class number of certain cyclotomic fields. https://arxiv.org/abs/2609.05950

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