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Watson transformations and class numbers of ternary quadratic forms
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 오병권 | - |
dc.contributor.author | Toshiya Kawakubo | - |
dc.date.accessioned | 2017-07-14T00:43:03Z | - |
dc.date.available | 2017-07-14T00:43:03Z | - |
dc.date.issued | 2017-02 | - |
dc.identifier.other | 000000141704 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121323 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2017. 2. 오병권. | - |
dc.description.abstract | The class number of an integral quadratic form is defined by the number of
inequivalent classes in its genus. Recently, Chan and Oh gave an explicit relation between the class number of a (positive definite integral) ternary quadratic form and the class number of its Watson transformation at an odd prime. In this thesis, we consider the case when the Watson transformation is taken at the prime 2 or 4 on arbitrary ternary quadratic forms and give an explicit relation under this situation. We finally give an effective inductive method on the computation of the class number of an arbitrary ternary quadratic form. As an example, we provide the class number formula for any Bell ternary quadratic form. | - |
dc.description.tableofcontents | 1 Introduction 1
2 Preliminaries 5 2.1 Quadratic spaces 5 2.2 Lattices on quadratic spaces 8 3 Watson transformations 11 3.1 Properties of Watson transformations 11 3.2 Definition of $gamma_k^L(K)$ 13 4 Labels of classes 15 4.1 Isometry groups 15 4.2 Definition of labels 20 4.3 The case when | - |
dc.description.tableofcontents | O(K) | - |
dc.description.tableofcontents | =24 22
4.4 The case when | - |
dc.description.tableofcontents | =16 28
4.5 The case when | - |
dc.description.tableofcontents | =12 38
4.6 The case when | - |
dc.description.tableofcontents | =8 42
4.7 The case when | - |
dc.description.tableofcontents | =4 69
5 Stable lattices 117 5.1 Labels of stable lattices 117 5.2 Information for exceptional cases 127 6 Applications 130 7 Appendix 134 Bibliography 150 국문초록 152 | - |
dc.format | application/pdf | - |
dc.format.extent | 2354714 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | ternary quadratic forms | - |
dc.subject | class number | - |
dc.subject | Watson transformation | - |
dc.subject.ddc | 510 | - |
dc.title | Watson transformations and class numbers of ternary quadratic forms | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 151 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2017-02 | - |
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