On the 2-primary Part of Tame Kernels of Real Quadratic Fields

Let F = Q（x/P）, where p = 8t ＋ 1 is a prime. In this paper, we prove that a speclm case of Qin＇s conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of Cohen and Lagarias on the existence of governing fields. We also characterize the 16-ra...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 32; no. 7; pp. 807 - 812
Main Authors Cheng, Xiao Yun, Guo, Xue Jun
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.07.2016
Springer Nature B.V
Subjects
Algebra
Fields (mathematics)
Formulas (mathematics)
Kernels
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Number theory
Studies
Symbols
Tame核
Texts
Theorems
实二次域
希尔伯特
方程
猜想
科恩
素数
class groups
Tame kernels
11R70
diophantine equations
19F15
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Summary:Let F = Q（x/P）, where p = 8t ＋ 1 is a prime. In this paper, we prove that a speclm case of Qin＇s conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of Cohen and Lagarias on the existence of governing fields. We also characterize the 16-rank of K2OF, which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not.
Bibliography:Tame kernels, class groups, diophantine equations
Let F = Q（x/P）, where p = 8t ＋ 1 is a prime. In this paper, we prove that a speclm case of Qin＇s conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of Cohen and Lagarias on the existence of governing fields. We also characterize the 16-rank of K2OF, which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not.
11-2039/O1
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-5053-y