Verfügbarkeit: Geometry of numbers | Technische Universität München

Geometry of numbers:

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Bibliographische Detailangaben
Beteiligte Personen:	Gruber, Peter M. 1941-2017 (VerfasserIn), Lekkerkerker, Cornelis G. 1922- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Amsterdam [u.a.] North-Holland 1987
Ausgabe:	2. ed.
Schriftenreihe:	North-Holland mathematical library 37
Schlagwörter:	Convexe lichamen Corps convexes Getaltheorie Géométrie des nombres Teoria Geometrica Dos Numeros Treillis, Théorie des Convex bodies Geometry of numbers Lattice theory Zahlentheorie Geometrie der Zahlen Konvexer Körper
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000431488&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 732 S.
ISBN:	0444701524

Internformat

MARC


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100	1		\|a Gruber, Peter M. \|d 1941-2017 \|e Verfasser \|0 (DE-588)11063814X \|4 aut
245	1	0	\|a Geometry of numbers \|c P. M. Gruber ; C. G. Lekkerkerker
250			\|a 2. ed.
264		1	\|a Amsterdam [u.a.] \|b North-Holland \|c 1987
300			\|a XV, 732 S.
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650		4	\|a Geometry of numbers
650		4	\|a Lattice theory
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Datensatz im Suchindex

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adam_text	CONTENTS Chapter 1. Preliminaries 1. Notations. Convex bodies 1 2. Ray sets and star bodies 14 3. Lattices 17 4. Algebraic Number fields 24 Supplement to Chapter 1 i. Preliminaries 32 Chapter 2. Convex bodies and lattice points 5. The fundamental theorem of Minkowski 39 6. Generalizations of the theorem of Blichfeldt 47 7. Generalizations of the theorem of Minkowski 50 8. A theorem of Redei and Hlawka 54 9. Successive minima of a convex body 58 10. Reduction theory 64 11. Successive minima of non convex sets 78 12. Extremal bodies 82 13. The inhomogeneous minimum 98 14. Polar reciprocal convex bodies 107 15. Compound convex bodies 114 16. Convex bodies and arbitrary lattices 123 Supplement to Chapter 2 ii. Fundamental theorems 126 lii. Lattice polytopes 135 iv. Large convex bodies 140 v. Reduction theory 147 vi. Tiling 164 xiii CONTENTS Chapter 3. The critical determinant, the covering constant and the inhomogeneous determinant of a set 17. Mahler s selection theorem. Critical determinant and absolute homoge¬ neous minimum. Critical lattices 177 18. The successive minima and the determinant of a set 188 19. The theorem of Minkowski Hlawka 199 20. Packing of convex bodies 218 21. Covering constant of a set. Covering by sets 228 22. Packings and coverings in the plane . 241 23. Inhomogeneous determinant of a set 250 24. A theorem of Mordell Siegel Hlawka Rogers 254 Supplement to Chapter 3 vii. Suprema and infima over lattices 259 viii. Packing 266 ix. Covering 279 Chapter 4. Star bodies 25. The functional A(S), r(S), /(/I), g(A) 290 26. Points of critical lattices on the boundary. Automorphic star bodies . . 300 27. Reducible and irreducible star bodies 309 28. Reduction of automorphic star bodies 316 Supplement to Chapter 4 x. Boundary lattice points 323 Chapter 5. Some methods 29. The critical determinant of a two dimensional star body. Methods of Mahler and Mordell 330 30. Some special two dimensional domains 338 31. The critical determinant of an n dimensional domain 340 32. Some special domains 348 33. A method of Blichfeldt. Density functions 352 34. A method of Blichfeldt and Mordell 357 35. A theorem of Macbeath 367 36. Comparison of star bodies in spaces of unequal dimensions 372 Note on Chapter 5 xiv CONTENTS Chapter 6. Homogeneous forms 37. Homogeneous forms, absolute minima, extreme forms 381 38. Spheres and quadratic forms 3X5 39. Extreme positive definite quadratic forms 393 40. Sums of powers of linear forms 411 41. Products of linear forms 422 42. Other homogeneous forms 432 43. Extreme forms. Isolated minima 441 44. Asymmetric and one sided inequalities 465 45. Diophantine approximation 474 Supplement to Chapter 6 xi. Packing of balls 499 xii. Extreme forms 528 xiii. Zeta functions 530 xiv. Homogeneous minima 535 Chapter 7. Inhomogeneous forms 46. Inhomogeneous minima of forms 549 47. Indefinite binary quadratic forms 552 48. Delone s algorithm. Lower bounds for n(Q, Y) 567 49. Inhomogeneous forms in more variables 578 50. Asymmetric inequalities 595 51. Inequalities with infinitely many solutions 599 Supplement to Chapter 7 xv. Covering with balls 613 xvi. Product of inhomogeneous linear forms 619 xvii. Inhomogeneous forms 627 xviii. Geometry of numbers in other spaces 629 Bibliography Books 632 Articles 636 Additional surveys 723 Index 726 XV
any_adam_object	1
author	Gruber, Peter M. 1941-2017 Lekkerkerker, Cornelis G. 1922-
author_GND	(DE-588)11063814X (DE-588)129419370
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ctrlnum	(OCoLC)246747507 (DE-599)BVBBV000691777
dewey-full	512/.72
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	512 - Algebra
dewey-raw	512/.72
dewey-search	512/.72
dewey-sort	3512 272
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	2. ed.
format	Book
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id	DE-604.BV000691777
illustrated	Not Illustrated
indexdate	2024-12-20T07:25:10Z
institution	BVB
isbn	0444701524
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-000431488
oclc_num	246747507
open_access_boolean
owner	DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-706 DE-83 DE-11 DE-188 DE-634
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physical	XV, 732 S.
publishDate	1987
publishDateSearch	1987
publishDateSort	1987
publisher	North-Holland
record_format	marc
series	North-Holland mathematical library
series2	North-Holland mathematical library
spellingShingle	Gruber, Peter M. 1941-2017 Lekkerkerker, Cornelis G. 1922- Geometry of numbers North-Holland mathematical library Convexe lichamen gtt Corps convexes Getaltheorie gtt Géométrie des nombres Teoria Geometrica Dos Numeros larpcal Treillis, Théorie des Convex bodies Geometry of numbers Lattice theory Zahlentheorie (DE-588)4067277-3 gnd Geometrie der Zahlen (DE-588)4227477-1 gnd Konvexer Körper (DE-588)4165214-9 gnd
subject_GND	(DE-588)4067277-3 (DE-588)4227477-1 (DE-588)4165214-9
title	Geometry of numbers
title_auth	Geometry of numbers
title_exact_search	Geometry of numbers
title_full	Geometry of numbers P. M. Gruber ; C. G. Lekkerkerker
title_fullStr	Geometry of numbers P. M. Gruber ; C. G. Lekkerkerker
title_full_unstemmed	Geometry of numbers P. M. Gruber ; C. G. Lekkerkerker
title_short	Geometry of numbers
title_sort	geometry of numbers
topic	Convexe lichamen gtt Corps convexes Getaltheorie gtt Géométrie des nombres Teoria Geometrica Dos Numeros larpcal Treillis, Théorie des Convex bodies Geometry of numbers Lattice theory Zahlentheorie (DE-588)4067277-3 gnd Geometrie der Zahlen (DE-588)4227477-1 gnd Konvexer Körper (DE-588)4165214-9 gnd
topic_facet	Convexe lichamen Corps convexes Getaltheorie Géométrie des nombres Teoria Geometrica Dos Numeros Treillis, Théorie des Convex bodies Geometry of numbers Lattice theory Zahlentheorie Geometrie der Zahlen Konvexer Körper
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000431488&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV023066394
work_keys_str_mv	AT gruberpeterm geometryofnumbers AT lekkerkerkercornelisg geometryofnumbers

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