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

Autor:	Kandhil, Neelam, Languasco, Alessandro, Moree, Pieter, Eddin, Sumaia Saad, Sedunova, Alisa
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Primary 11R18 11R29 Secondary 11R47 11Y60
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jmaa.2024.128368
Popis:	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. Comment: 23 pages, 4 figures, 3 tables; to appear in Journal of Mathematical Analysis and Applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.13829 Zobrazit plný text záznamu View this record from Arxiv