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The number of minimum points of a positive quadratic form

100%

Watson G. L.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction.......................................................................................6 1. Definition of certain special forms...........................................6 2. Statement of results...................................................................8 3. Proof of Theorem 2.....................................................................9 4. Preliminaries for Theorem 1.....................................................10 5. Further preliminaries for Theorem 1.......................................15 6. Construction for Theorem 1......................................................18 7. The case $B_4 ⊄ ƒ_n, C_5 ⊄ ƒ_n$ of Theorem 1..............21 8. The case $B_5 ⊄ ƒ_n$ of Theorem 1....................................24 9. Further construction for the case $B_5 ⊂ ƒ_n ≥ 7$............26 10. The case $E_6 ⊄ ƒ_n$...........................................................30 11. Preliminaries for the case $E_6 ⊂ ƒ_n$.............................32 12. Proof of Theorem 1 for $E_8 ⊄ ƒ_n$ and for n ≥ 10.........34 13. Completion of proof of Theorem 1........................................38 14. Conclusion.................................................................................40 References.......................................................................................42

2

The least common denominator of the coefficients of a perfect quadratic form

42%

Watson G. L.

Acta Arithmetica

|

1971

|

tom 18

|

nr 1

29-36

3

Existence of an indecomposable positive quadratic form in a given genus of rank at least 14

42%

Watson G. L.

Acta Arithmetica

|

1979

|

tom 35

|

nr 1

55-100

4

One-class genera of positive quaternary quadratic forms

36%

Watson G. L.

Acta Arithmetica

|

1973-1974

|

tom 24

|

nr 5

461-475

5

Transformations of a quadratic form which do not increase the class-number II

36%

Watson G. L.

Acta Arithmetica

|

1975

|

tom 27

|

nr 1

171-189

6

One-class genera of positive quadratic forms in at least five variables

36%

Watson G. L.

Acta Arithmetica

|

1974-1975

|

tom 26

|

nr 3

309-327

Ograniczanie wyników

5 Acta Arithmetica

6 Watson G. L.

1 1979

2 1975

1 1974

2 1971

The number of minimum points of a positive quadratic form

The least common denominator of the coefficients of a perfect quadratic form

Existence of an indecomposable positive quadratic form in a given genus of rank at least 14

One-class genera of positive quaternary quadratic forms

Transformations of a quadratic form which do not increase the class-number II

One-class genera of positive quadratic forms in at least five variables