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Arithmetic properties of the representations of ternary quadratic forms

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Authors
주장원
Advisor
오병권
Major
자연과학대학 수리과학부
Issue Date
2016-08
Publisher
서울대학교 대학원
Keywords
Representation of ternary quadratic formsWatson transformationsGraph of ternary quadratic formsGenus-correspondencesComplete system of spinor exceptional integers
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 오병권.
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.
Language
English
URI
http://hdl.handle.net/10371/121315
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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