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arXiv · 2402.13829

The Kummer ratio of the relative class number for prime cyclotomic fields

Neelam Kandhil·Alessandro Languasco·Pieter Moree·Sumaia Saad Eddin·Alisa Sedunova
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Abstract

Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three scenarios: no Siegel zero, presence of Siegel zero and assuming the Riemann Hypothesis for the Dirichlet $L$-series attached to odd characters only. The numerical work in this paper extends and improves on our earlier preprint (arXiv:1908.01152) and demonstrates our theoretical results.

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Neelam Kandhil, Alessandro Languasco, Pieter Moree, Sumaia Saad Eddin, Alisa Sedunova. 2024-03-28. The Kummer ratio of the relative class number for prime cyclotomic fields. https://doi.org/10.1016/j.jmaa.2024.128368

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