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Geometry of numbers
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Groningen, Amsterdam,
Wolters-Noordhoff; North-Holland Pub. Co.,
1969 [1970]
|
| Colección: | Bibliotheca mathematica ;
v. 8. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Geometry of Numbers; Copyright Page; PREFACE; Table of Contents; CHAPTER 1. PRELIMINARIES; 1. Notations. Convex bodies; 2. Ray sets and star bodies; 3. Lattices; 4. Algebraic number fields; CHAPTER 2. CONVEX BODIES AND LATTICE POINTS; 5. The fundamental theorem of Minkowski; 6. Generalizations of the theorem of Blichfeldt; 7. Generalizations of the theorem of Minkowski; 8. A theorem of R�edei and Hlawka; 9. Successive minima of a convex body; 10. Reduction theory; 11. Successive minima of non-convex sets; 12. Extremal bodies; 13. The inhomogeneous minimum
- 14. Polar reciprocal convex bodies15. Compound convex bodies; 16. Convex bodies and arbitrary lattices; CHAPTER 3. THE CRITICAL DETERMINANT, THE COVERING CONSTANTAND THE INHOMOGENEOUS DETERMINANT OF A SET; 17. Mahler's selection theorem. Critical determinant and absolute homogeneousminimum. Critical lattices; 18. The successive minima and the determinant of a set; 19. The theorem of Minkowski-Hlawka; 20. Packing of convex bodies; 21. Covering constant of a set. Covering by sets; 22. Packings and coverings in the plane; 23. Inhomogeneous determinant of a set
- 24. A theorem of Mordell-Siegel-Hlawka-RogersCHAPTER 4. STAR BODIES; 25. Thefunctionate; 26. Points of critical lattices on the boundary. Automorphic star bodies; 27. Reducible and irreducible star bodies; 28. Reduction of automorphic star bodies; CHAPTER 5. SOME METHODS; 29. The critical determinant of a two-dimensional star body. Methodsof Mahler and Mordell; 30. Some special two-dimensional domains; 31. The critical determinant of ann-dimensional domain; 32. Some special domains; 33. A method of Blichfeldt. Density functions; 34. A method of Blichfeldt and Mordell
- 35. A theorem of Macbeath36. Comparison of star bodies in spaces of unequal dimensions; CHAPTER 6. HOMOGENEOUS FORMS; 37. Homogeneous forms, absolute minima, extreme forms; 38� Spheres and quadratic forms; 39. Extreme positive definite quadratic forms; 40. Sums of powers of linear forms; 41. Products of linear forms; 42. Other homogeneous forms; 43. Extreme forms. Isolated minima; 44. Asymmetric and one-sided inequalities; 45. Diophantine approximation; CHAPTER 7. INHOMOGENEOUS FORMS; 46. Inhomogeneous minima of forms; 47. Indefinite binary quadratic forms
- 48. Delone's algorithm. Lower boundsfor49. Inhomogeneous forms in more variables; 50. Asymmetric inequalities; 51. Inequalities with infinitely many solutions; BIBLIOGRAPHY; INDEX