S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
Almost 2-universal quinary quadratic forms
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2017. 2. 오병권.
- In this thesis, we consider various problems on the representations of binary quadratic forms by positive definite quinary quadratic forms. A (positive definite integral) quadratic form is called almost 2-universal if it represents all (positive definite integral) binary quadratic forms but finitely many up to isometry. We prove that three candidates of almost 2-universal quinary diagonal quadratic forms are indeed almost 2-universal. We also prove that there are at most 16 almost 2-universal quinary quadratic forms having exactly only one exception, and prove the almost 2-universalities of some candidates. A (positive definite integral) quadratic form is called diagonally 2-universal if it represents all (positive definite integral) binary diagonal quadratic forms. We prove that there are at most 34 diagonally 2-universal quinary quadratic forms, and prove the diagonally 2-universalities of 29 candidates among them.