Geometry of numbers:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
North-Holland
1987
|
| Edition: | 2. ed. |
| Series: | North-Holland mathematical library
37 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 732 S. |
| ISBN: | 0444701524 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000691777 | ||
| 003 | DE-604 | ||
| 005 | 20210607 | ||
| 007 | t | ||
| 008 | 880120s1987 |||| 00||| eng d | ||
| 020 | |a 0444701524 |9 0-444-70152-4 | ||
| 035 | |a (OCoLC)246747507 | ||
| 035 | |a (DE-599)BVBBV000691777 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91G |a DE-384 |a DE-703 |a DE-739 |a DE-355 |a DE-20 |a DE-824 |a DE-29T |a DE-706 |a DE-83 |a DE-11 |a DE-188 |a DE-634 | ||
| 050 | 0 | |a QA241.5 | |
| 082 | 0 | |a 512/.72 |2 19 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 084 | |a 10Exx |2 msc | ||
| 084 | |a MAT 104f |2 stub | ||
| 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. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a North-Holland mathematical library |v 37 | |
| 650 | 7 | |a Convexe lichamen |2 gtt | |
| 650 | 4 | |a Corps convexes | |
| 650 | 7 | |a Getaltheorie |2 gtt | |
| 650 | 4 | |a Géométrie des nombres | |
| 650 | 7 | |a Teoria Geometrica Dos Numeros |2 larpcal | |
| 650 | 4 | |a Treillis, Théorie des | |
| 650 | 4 | |a Convex bodies | |
| 650 | 4 | |a Geometry of numbers | |
| 650 | 4 | |a Lattice theory | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrie der Zahlen |0 (DE-588)4227477-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konvexer Körper |0 (DE-588)4165214-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geometrie der Zahlen |0 (DE-588)4227477-1 |D s |
| 689 | 0 | 1 | |a Konvexer Körper |0 (DE-588)4165214-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Lekkerkerker, Cornelis G. |d 1922- |e Verfasser |0 (DE-588)129419370 |4 aut | |
| 830 | 0 | |a North-Holland mathematical library |v 37 |w (DE-604)BV023066394 |9 37 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-000431488 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804115140231036928 |
|---|---|
| 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 |
| author_facet | Gruber, Peter M. 1941-2017 Lekkerkerker, Cornelis G. 1922- |
| author_role | aut aut |
| author_sort | Gruber, Peter M. 1941-2017 |
| author_variant | p m g pm pmg c g l cg cgl |
| building | Verbundindex |
| bvnumber | BV000691777 |
| callnumber-first | Q - Science |
| callnumber-label | QA241 |
| callnumber-raw | QA241.5 |
| callnumber-search | QA241.5 |
| callnumber-sort | QA 3241.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 380 |
| classification_tum | MAT 104f |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02359nam a2200601 cb4500</leader><controlfield tag="001">BV000691777</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210607 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">880120s1987 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0444701524</subfield><subfield code="9">0-444-70152-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246747507</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000691777</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA241.5</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.72</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">10Exx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 104f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gruber, Peter M.</subfield><subfield code="d">1941-2017</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)11063814X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometry of numbers</subfield><subfield code="c">P. M. Gruber ; C. G. Lekkerkerker</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam [u.a.]</subfield><subfield code="b">North-Holland</subfield><subfield code="c">1987</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 732 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">North-Holland mathematical library</subfield><subfield code="v">37</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Convexe lichamen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Corps convexes</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Getaltheorie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Géométrie des nombres</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Teoria Geometrica Dos Numeros</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Treillis, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex bodies</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry of numbers</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lattice theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrie der Zahlen</subfield><subfield code="0">(DE-588)4227477-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexer Körper</subfield><subfield code="0">(DE-588)4165214-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Geometrie der Zahlen</subfield><subfield code="0">(DE-588)4227477-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Konvexer Körper</subfield><subfield code="0">(DE-588)4165214-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lekkerkerker, Cornelis G.</subfield><subfield code="d">1922-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)129419370</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">North-Holland mathematical library</subfield><subfield code="v">37</subfield><subfield code="w">(DE-604)BV023066394</subfield><subfield code="9">37</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-000431488</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV000691777 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:53Z |
| 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 |
| owner_facet | 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 |
| 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 |
| spelling | Gruber, Peter M. 1941-2017 Verfasser (DE-588)11063814X aut Geometry of numbers P. M. Gruber ; C. G. Lekkerkerker 2. ed. Amsterdam [u.a.] North-Holland 1987 XV, 732 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 37 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 rswk-swf Geometrie der Zahlen (DE-588)4227477-1 gnd rswk-swf Konvexer Körper (DE-588)4165214-9 gnd rswk-swf Geometrie der Zahlen (DE-588)4227477-1 s Konvexer Körper (DE-588)4165214-9 s DE-604 Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Lekkerkerker, Cornelis G. 1922- Verfasser (DE-588)129419370 aut North-Holland mathematical library 37 (DE-604)BV023066394 37 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |