Characters and cyclotomic fields in finite geometry:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Lecture notes in mathematics
1797 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981316&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VIII, 100 S. |
| ISBN: | 354044243X |
Internformat
MARC
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| 100 | 1 | |a Schmidt, Bernhard |d 1967- |e Verfasser |0 (DE-588)130325341 |4 aut | |
| 245 | 1 | 0 | |a Characters and cyclotomic fields in finite geometry |c Bernhard Schmidt |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a VIII, 100 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1797 | |
| 650 | 7 | |a Combinatieleer |2 gtt | |
| 650 | 4 | |a Cyclotomie | |
| 650 | 4 | |a Ensembles de différence | |
| 650 | 4 | |a Géométries finies | |
| 650 | 4 | |a Cyclotomy | |
| 650 | 4 | |a Difference sets | |
| 650 | 4 | |a Finite geometries | |
| 650 | 0 | 7 | |a Hadamard-Matrix |0 (DE-588)4158663-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differenzenmenge |0 (DE-588)4226544-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Endliche Geometrie |0 (DE-588)4014650-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zyklischer Code |0 (DE-588)4283233-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kreiskörper |0 (DE-588)4165607-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Endliche Geometrie |0 (DE-588)4014650-9 |D s |
| 689 | 0 | 1 | |a Kreiskörper |0 (DE-588)4165607-6 |D s |
| 689 | 0 | 2 | |a Hadamard-Matrix |0 (DE-588)4158663-3 |D s |
| 689 | 0 | 3 | |a Differenzenmenge |0 (DE-588)4226544-7 |D s |
| 689 | 0 | 4 | |a Zyklischer Code |0 (DE-588)4283233-0 |D s |
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| 830 | 0 | |a Lecture notes in mathematics |v 1797 |w (DE-604)BV000676446 |9 1797 | |
| 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=009981316&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009981316 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-1797 |
|---|---|
| DE-BY-TUM_katkey | 1320667 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020130438 |
| _version_ | 1821940312690393089 |
| adam_text | Contents
1 Introduction 1
1.1 The nature of the problems 2
1.2 The combinatorial structures in question 4
1.2.1 Designs 4
1.2.2 Difference Sets 6
1.2.3 Projective planes and planar functions 7
1.2.4 Projective geometries and Singer difference sets .... 9
1.2.5 Hadamard matrices and weighing matrices 10
1.2.6 Irreducible cyclic codes, two intersection sets and sub
difference sets 11
1.3 Group rings, characters, Fourier analysis 14
1.4 Number theoretic tools 19
1.5 Algebraic combinatorial tools 24
2 The field descent 27
2.1 The fixing theorem 27
2.2 Prescribed absolute value 31
2.3 Bounding the absolute value 36
2.4 The modulus equation and class groups 37
2.4.1 Class groups of cyclotomic fields 39
2.4.2 Class groups of CM fields 44
2.4.3 p ranks and class fields towers 48
3 Exponent bounds 53
3.1 Self conjugacy exponent bounds 53
3.1.1 Turyn s exponent bound 54
3.1.2 The coset intersection lemma 55
3.1.3 McFarland difference sets 57
3.1.4 Semiregular relative difference sets 58
3.1.5 Two recent families of difference sets 61
3.1.6 Chen difference sets 62
3.1.7 Davis Jedwab difference sets 66
3.2 Field descent exponent bounds 67
VIII CONTENTS
3.2.1 A general exponent bound for difference sets 68
3.2.2 Difference sets with gcd(u, n) 1 69
3.2.3 Towards Ryser s conjecture 71
3.2.4 Circulant Hadamard matrices and
Barker sequences 73
3.2.5 Relative difference sets and planar functions 74
3.2.6 Group invariant weighing matrices 77
4 Two weight irreducible cyclic codes 79
4.1 A necessary and sufficient condition 80
4.2 All two weight irreducible cyclic codes? 83
4.2.1 Subfield and semiprimitive codes 83
4.2.2 The exceptional codes 84
4.3 Partial proof of Conjecture 4.2.4 85
4.4 Two intersection sets and sub difference sets 88
4.4.1 Two intersection sets in PG(m — l,q) 88
4.4.2 Sub difference sets of Singer difference sets 88
Bibliography 91
Index 99
|
| any_adam_object | 1 |
| author | Schmidt, Bernhard 1967- |
| author_GND | (DE-588)130325341 |
| author_facet | Schmidt, Bernhard 1967- |
| author_role | aut |
| author_sort | Schmidt, Bernhard 1967- |
| author_variant | b s bs |
| building | Verbundindex |
| bvnumber | BV014728461 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 180 |
| classification_tum | MAT 052f MAT 125f MAT 514f |
| ctrlnum | (OCoLC)50520404 (DE-599)BVBBV014728461 |
| dewey-full | 516/.13 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry 510 - Mathematics |
| dewey-raw | 516/.13 510 |
| dewey-search | 516/.13 510 |
| dewey-sort | 3516 213 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014728461 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:07:01Z |
| institution | BVB |
| isbn | 354044243X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009981316 |
| oclc_num | 50520404 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-739 DE-824 DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-739 DE-824 DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | VIII, 100 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Schmidt, Bernhard 1967- Characters and cyclotomic fields in finite geometry Lecture notes in mathematics Combinatieleer gtt Cyclotomie Ensembles de différence Géométries finies Cyclotomy Difference sets Finite geometries Hadamard-Matrix (DE-588)4158663-3 gnd Differenzenmenge (DE-588)4226544-7 gnd Endliche Geometrie (DE-588)4014650-9 gnd Zyklischer Code (DE-588)4283233-0 gnd Kreiskörper (DE-588)4165607-6 gnd |
| subject_GND | (DE-588)4158663-3 (DE-588)4226544-7 (DE-588)4014650-9 (DE-588)4283233-0 (DE-588)4165607-6 |
| title | Characters and cyclotomic fields in finite geometry |
| title_auth | Characters and cyclotomic fields in finite geometry |
| title_exact_search | Characters and cyclotomic fields in finite geometry |
| title_full | Characters and cyclotomic fields in finite geometry Bernhard Schmidt |
| title_fullStr | Characters and cyclotomic fields in finite geometry Bernhard Schmidt |
| title_full_unstemmed | Characters and cyclotomic fields in finite geometry Bernhard Schmidt |
| title_short | Characters and cyclotomic fields in finite geometry |
| title_sort | characters and cyclotomic fields in finite geometry |
| topic | Combinatieleer gtt Cyclotomie Ensembles de différence Géométries finies Cyclotomy Difference sets Finite geometries Hadamard-Matrix (DE-588)4158663-3 gnd Differenzenmenge (DE-588)4226544-7 gnd Endliche Geometrie (DE-588)4014650-9 gnd Zyklischer Code (DE-588)4283233-0 gnd Kreiskörper (DE-588)4165607-6 gnd |
| topic_facet | Combinatieleer Cyclotomie Ensembles de différence Géométries finies Cyclotomy Difference sets Finite geometries Hadamard-Matrix Differenzenmenge Endliche Geometrie Zyklischer Code Kreiskörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981316&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT schmidtbernhard charactersandcyclotomicfieldsinfinitegeometry |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 999-1797
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |