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Arithmetic properties of the representations of ternary quadratic forms
DC Field | Value | Language |
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dc.contributor.advisor | 오병권 | - |
dc.contributor.author | 주장원 | - |
dc.date.accessioned | 2017-07-14T00:42:37Z | - |
dc.date.available | 2017-07-14T00:42:37Z | - |
dc.date.issued | 2016-08 | - |
dc.identifier.other | 000000136406 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121315 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 오병권. | - |
dc.description.abstract | In this thesis, we discuss some arithmetic relations on the representations of (positive definite integral) ternary quadratic forms. Let r(n,f) be the number of representations of an integer n by a ternary quadratic form f and let p be a prime such that f is isotropic over Z_p. We show that under some restrictions, r(n,f) can be expressed as a summation of r(pn,g)'s and r(p^3n,g)'s with some extra term that can be explicitly computable, where each quadratic form g is contained in the same genus determined by f and p.
In the second part of the thesis, we discuss genus-correspondences between ternary quadratic forms respecting spinor genus. We modify the conjecture given by Jagy and prove this modified version. We also construct genus-correspondences satisfying some additional properties. In particular, we construct infinite family of genera of ternary quadratic forms that possess (absolutely) complete systems of spinor exceptional integers. | - |
dc.description.tableofcontents | Chapter 1 Introduction 1
Chapter 2 Preliminaries 6 2.1 Definitions 6 2.2 Spinor norms of local integral rotations 11 2.3 Spinor exceptional integers 16 Chapter 3 Watson transformations 21 3.1 H-type lattices 21 3.2 Generalization of Watson transformations 24 Chapter 4 Finite (Multi-) graphs of ternary forms 33 4.1 Definition of the graph G_{L,p}(m) 33 4.2 Connected components 36 4.3 Simplicity and Regularity 47 Chapter 5 Arithmetic relations of representations 54 5.1 The case when m = 0 55 5.2 The case when m = 1 60 Chapter 6 Genus-correspondences & Representations 68 6.1 Genus-correspondences 68 6.2 Reduced genera 73 6.3 Spinor character theory 76 Bibliography 82 국문 초록 84 | - |
dc.format | application/pdf | - |
dc.format.extent | 1394368 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Representation of ternary quadratic forms | - |
dc.subject | Watson transformations | - |
dc.subject | Graph of ternary quadratic forms | - |
dc.subject | Genus-correspondences | - |
dc.subject | Complete system of spinor exceptional integers | - |
dc.subject.ddc | 510 | - |
dc.title | Arithmetic properties of the representations of ternary quadratic forms | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 83 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2016-08 | - |
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