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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| Published in | Acta mathematica Sinica. English series Vol. 32; no. 7; pp. 807 - 812 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Beijing
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.07.2016
Springer Nature B.V |
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| Abstract | 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. |
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| AbstractList | Let
, where
p
= 8
t
+1 is a prime. In this paper, we prove that a special case of Qin’s conjecture on the possible structure of the 2-primary part of
K
2
O
F
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
K
2
O
F
, which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not. 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. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Let ..., where p = 8t+1 is a prime. In this paper, we prove that a special case of Qin's conjecture on the possible structure of the 2-primary part of K 2 O F 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 K 2 O F, which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).Let ..., where p = 8t+1 is a prime. In this paper, we prove that a special case of Qin's conjecture on the possible structure of the 2-primary part of K sub(2) O sub( )Fup 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 K sub(2) O sub( )F which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not. |
| Author | Xiao Yun CHENG Xue Jun GUO |
| AuthorAffiliation | School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China |
| Author_xml | – sequence: 1 givenname: Xiao Yun surname: Cheng fullname: Cheng, Xiao Yun email: xycheng@nuaa.edu.cn organization: School of Science, Nanjing University of Aeronautics and Astronautics – sequence: 2 givenname: Xue Jun surname: Guo fullname: Guo, Xue Jun organization: Department of Mathematics, Nanjing University |
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| Cites_doi | 10.1090/S0025-5718-99-01000-5 10.4064/aa152-4-4 10.1080/00927870701872463 10.4153/CMB-2004-042-1 10.1007/BF00535049 10.1016/0022-314X(86)90077-6 10.4064/aa136-2-3 10.1080/00927870701776797 10.4064/aa116-3-2 10.4064/aa102-1-4 10.1016/S0022-314X(02)00045-8 10.1016/j.jalgebra.2004.10.024 10.1142/0663 10.1007/BF02621923 10.4064/aa113-3-1 10.4064/aa-72-4-323-333 10.4064/aa-69-2-153-169 |
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| Copyright | Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2016 |
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| DOI | 10.1007/s10114-016-5053-y |
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| Keywords | class groups Tame kernels 11R70 diophantine equations 19F15 |
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| Notes | 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 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
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| Snippet | 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... Let , where p = 8 t +1 is a prime. In this paper, we prove that a special case of Qin’s conjecture on the possible structure of the 2-primary part of K 2 O F... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Let ..., where p = 8t+1 is a prime. In this paper, we prove that a special case of... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).Let ..., where p = 8t+1 is a prime. In this paper, we prove that a special case of... |
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| SubjectTerms | 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 |
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| Title | On the 2-primary Part of Tame Kernels of Real Quadratic Fields |
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