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Watson transformations and class numbers of ternary quadratic forms
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- Authors
- Advisor
- 오병권
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2017-02
- Publisher
- 서울대학교 대학원
- Keywords
- ternary quadratic forms ; class number ; Watson transformation
- Description
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2017. 2. 오병권.
- 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.
- Language
- English
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