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Representations of squares by positive ternary quadratic forms
삼변수 양 이차형식에 의한 제곱수의 표현

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dc.contributor.advisor오병권-
dc.contributor.author김경민-
dc.date.accessioned2017-10-27T17:13:42Z-
dc.date.available2017-10-27T17:13:42Z-
dc.date.issued2017-08-
dc.identifier.other000000145921-
dc.identifier.urihttps://hdl.handle.net/10371/137163-
dc.description학위논문 (박사)-- 서울대학교 대학원 자연과학대학 수리과학부, 2017. 8. 오병권.-
dc.description.abstractIn this thesis, we study various properties of representations of squares by ternary quadratic forms.
A (positive definite integral) ternary quadratic form is called strongly S-regular if it satisfies a regularity property on the number of representations of squares of integers. We explain the relation between the strongly S-regularity and the conjecture given by Cooper and Lam, and we resolve their conjecture completely. We prove that there are only finitely many strongly S-regular ternary forms up to isometry if the minimum of the non zero squares that are represented by the form is fixed. In particular, we show that there are exactly 207 non-classic integral strongly S-regular ternary quadratic forms representing one.
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dc.description.tableofcontentsContents
Abstract i
1 Introduction 1
2 Preliminaries 6
2.1 Definitions 6
2.2 Splitting integers 12
2.3 The Minkowski-Siegel formula 13
2.4 Calculations of local densities 16
3 Representations of squares by ternary forms 20
3.1 Indistinguishable by squares 20
3.2 The Cooper and Lam's conjecture 24
4 Strongly S-regular ternary forms 35
4.1 Some properties of strongly S-regular ternary forms 35
4.2 Strongly S-regular ternary forms representing 1 41
4.3 Nontrivial strongly S-regular ternary forms 48
5 Strongly regularity on square classes 56
5.1 Strongly S_t-regular ternary forms 56
5.2 Strongly spinor S_t-regular ternary forms 58
Abstract (in Korean) 64
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dc.formatapplication/pdf-
dc.format.extent2048161 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectRepresentations of ternary quadratic forms-
dc.subjectsquares-
dc.subject.ddc510-
dc.titleRepresentations of squares by positive ternary quadratic forms-
dc.title.alternative삼변수 양 이차형식에 의한 제곱수의 표현-
dc.typeThesis-
dc.contributor.AlternativeAuthorKyoungmin Kim-
dc.description.degreeDoctor-
dc.contributor.affiliation자연과학대학 수리과학부-
dc.date.awarded2017-08-
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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