Perfect Lattices in Euclidean Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
327 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices |
| Beschreibung: | 1 Online-Ressource (XXII, 526 p) |
| ISBN: | 9783662051672 9783642079214 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-05167-2 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423346 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2003 |||| o||u| ||||||eng d | ||
| 020 | |a 9783662051672 |c Online |9 978-3-662-05167-2 | ||
| 020 | |a 9783642079214 |c Print |9 978-3-642-07921-4 | ||
| 024 | 7 | |a 10.1007/978-3-662-05167-2 |2 doi | |
| 035 | |a (OCoLC)863899770 | ||
| 035 | |a (DE-599)BVBBV042423346 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512.7 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Martinet, Jacques |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Perfect Lattices in Euclidean Spaces |c by Jacques Martinet |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 2003 | |
| 300 | |a 1 Online-Ressource (XXII, 526 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 327 |x 0072-7830 | |
| 500 | |a Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Gitter |g Mathematik |0 (DE-588)4157375-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Euklidischer Raum |0 (DE-588)4309127-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gitter |g Mathematik |0 (DE-588)4157375-4 |D s |
| 689 | 0 | 1 | |a Euklidischer Raum |0 (DE-588)4309127-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-662-05167-2 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858763 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153098970595328 |
|---|---|
| any_adam_object | |
| author | Martinet, Jacques |
| author_facet | Martinet, Jacques |
| author_role | aut |
| author_sort | Martinet, Jacques |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV042423346 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863899770 (DE-599)BVBBV042423346 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-05167-2 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02899nmm a2200493zcb4500</leader><controlfield tag="001">BV042423346</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2003 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662051672</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-662-05167-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642079214</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-07921-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-662-05167-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863899770</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423346</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Martinet, Jacques</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Perfect Lattices in Euclidean Spaces</subfield><subfield code="c">by Jacques Martinet</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XXII, 526 p)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics</subfield><subfield code="v">327</subfield><subfield code="x">0072-7830</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gitter</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4157375-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Euklidischer Raum</subfield><subfield code="0">(DE-588)4309127-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Gitter</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4157375-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Euklidischer Raum</subfield><subfield code="0">(DE-588)4309127-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-662-05167-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858763</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.BV042423346 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662051672 9783642079214 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858763 |
| oclc_num | 863899770 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XXII, 526 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Martinet, Jacques Verfasser aut Perfect Lattices in Euclidean Spaces by Jacques Martinet Berlin, Heidelberg Springer Berlin Heidelberg 2003 1 Online-Ressource (XXII, 526 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 327 0072-7830 Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices Mathematics Combinatorics Number theory Number Theory Mathematik Gitter Mathematik (DE-588)4157375-4 gnd rswk-swf Euklidischer Raum (DE-588)4309127-1 gnd rswk-swf Gitter Mathematik (DE-588)4157375-4 s Euklidischer Raum (DE-588)4309127-1 s 1\p DE-604 https://doi.org/10.1007/978-3-662-05167-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Martinet, Jacques Perfect Lattices in Euclidean Spaces Mathematics Combinatorics Number theory Number Theory Mathematik Gitter Mathematik (DE-588)4157375-4 gnd Euklidischer Raum (DE-588)4309127-1 gnd |
| subject_GND | (DE-588)4157375-4 (DE-588)4309127-1 |
| title | Perfect Lattices in Euclidean Spaces |
| title_auth | Perfect Lattices in Euclidean Spaces |
| title_exact_search | Perfect Lattices in Euclidean Spaces |
| title_full | Perfect Lattices in Euclidean Spaces by Jacques Martinet |
| title_fullStr | Perfect Lattices in Euclidean Spaces by Jacques Martinet |
| title_full_unstemmed | Perfect Lattices in Euclidean Spaces by Jacques Martinet |
| title_short | Perfect Lattices in Euclidean Spaces |
| title_sort | perfect lattices in euclidean spaces |
| topic | Mathematics Combinatorics Number theory Number Theory Mathematik Gitter Mathematik (DE-588)4157375-4 gnd Euklidischer Raum (DE-588)4309127-1 gnd |
| topic_facet | Mathematics Combinatorics Number theory Number Theory Mathematik Gitter Mathematik Euklidischer Raum |
| url | https://doi.org/10.1007/978-3-662-05167-2 |
| work_keys_str_mv | AT martinetjacques perfectlatticesineuclideanspaces |