Congruences for the class numbers of real cyclic sextic number fields
type: Item
instance of: scholarly article
title: Congruences for the class numbers of real cyclic sextic number fields
zbMATH Open document ID: 0991.11057
DOI: 10.1007/BF02889501
author: Tong Liu
published in: Science in China. Series A
publication date: 2002-08-26T00:00:00Z
review text: Extending results on quadratic and cyclic quartic fields the author studies the class number \(h\) of real cyclic sextic number fields \(K\). Seven congruences are obtained. In particular when the conductor of \(K\) is a prime \(p\), then \[ C\cdot h^-\equiv B_{{p-1}\over{6}}\cdot B_{{5(p-1)}\over{6}} (\bmod p) \] where \(C\) is an explicitly given constant.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R21
Mathematics Subject Classification ID: 11B68
zbMATH DE Number: 1439350
zbMATH Keywords: class numbers
zbMATH Keywords: real cyclic sextic fields
reviewed by: István Gaál
MaRDI profile type: Publication
cites work: The class-number of real quadratic number fields
cites work: Congruences for the class number of quadratic fields
cites work: Q3767417
cites work: The determination of units in real cyclic sextic fields
cites work: Q3943047
cites work: Regulatorabschätzungen für total reelle algebraische Zahlkörper
description: scientific article; zbMATH DE number 1439350