Title Page
Abstract
Contents
Chapter 1. Introduction 11
Chapter 2. Preliminaries 15
2.1. Representations of quadratic spaces 15
2.2. Representations of quadratic lattices 24
2.3. n-universality and primitive n-universality 37
Chapter 3. Primitively n-universal Zp-lattices of minimal rank[이미지참조] 43
3.1. Generalities 43
3.2. Primitively n-universal Zp-lattices of minimal rank for an odd prime p[이미지참조] 46
3.3. Primitively n-universal Z₂-lattices of minimal rank 48
3.3.1. Classification of primitively 2-universal Z₂-lattices 50
3.3.2. The minimal rank of primitively 3-universal Z₂-lattices 53
3.3.3. Primitive 4-universality over Z₂ 55
3.3.4. The minimal rank of primitively n-universal Z₂-lattices for n ≥ 5 68
Chapter 4. Primitively 2-universal Z-lattices of rank six 71
4.1. The minimal rank of primitively 2-universal Z-lattices 71
4.2. Candidates of primitively 2-universal senary Z-lattices 73
4.3. The proof of primitive 2-universality (ordinary cases) 78
4.3.1. Class number one case 78
4.3.2. Class number one 5-section case 80
4.3.3. A class number one superlattice of the 5-section case 89
4.4. The proof of primitive 2-universality (exceptional cases) 95
4.4.1. Type Bii[이미지참조] 99
4.4.2. Type Dii[이미지참조] 101
4.4.3. Type Diii[이미지참조] 103
4.4.4. Type Hi[이미지참조] 108
4.4.5. Type Hii[이미지참조] 114
4.4.6. Type Hiii[이미지참조] 118
4.4.7. Type Hiv[이미지참조] 121
4.4.8. Type Iii[이미지참조] 124
4.4.9. Type Iiii[이미지참조] 128
4.4.10. Type J 132
4.4.11. Lattices D₅iii and I₅ii[이미지참조] 136
Bibliography 145
국문초록 148