CONTENTS
Preface v
1. Heilbronn' s Theore m
2. Th e Heilbron n Alternativ e Lemm a 3
3. Vinogradov' s Lemm a 4
4. Abou t Sum s 1 If-H" 1 5
5. Abou t Sum s 2 e(aw 2) 6
6. Proo f o f th e Heilbron n Alternativ e Lemm a 8
7. Fractiona l Part s o f Polynomial s 9
8. A Genera l Alternativ e Lemm a 1
9. Sum s 2 ||£.| | -1 Agai n 1
10. Estimatio n o f Wey l Sum s 1
11. Wha t Happen s i f th e Wey l Sum s ar e Larg e 1
12. Proo f o f th e Genera l Alternativ e Theore m 2
13. Simultaneou s Approximatio n 2
14. A Reductio n 2
15. A Vinogrado v Lemm a 2
16. Proo f o f th e Alternativ e Lemm a o n Simultaneou s Approximatio n 2
17. O n max||a.rz 2|| 2
18. A Determinan t Argumen t 3
19. Proo f o f th e Thre e Alternative s Lemm a 3
20. Quadrati c Polynomial s i n Severa l Variable s 3
21. Proof s fo r Quadrati c Polynomial s 3
References 4
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