The Kummer ratio of the relative class number for prime cyclotomic fields
Number Theory
2025-02-07 v3
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 -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.
Keywords
Cite
@article{arxiv.2402.13829,
title = {The Kummer ratio of the relative class number for prime cyclotomic fields},
author = {Neelam Kandhil and Alessandro Languasco and Pieter Moree and Sumaia Saad Eddin and Alisa Sedunova},
journal= {arXiv preprint arXiv:2402.13829},
year = {2025}
}
Comments
23 pages, 4 figures, 3 tables; to appear in Journal of Mathematical Analysis and Applications