Dickson polynomials
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| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow
Longman Scientific & Technical
1993
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman monographs and surveys in pure and applied mathematics
65 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Lidl, Rudolf |d 1948- |e Verfasser |0 (DE-588)136240755 |4 aut | |
| 245 | 1 | 0 | |a Dickson polynomials |c R. Lidl ; G. L. Mullen ; G. Turnwald |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow |b Longman Scientific & Technical |c 1993 | |
| 300 | |a 207 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 65 | |
| 500 | |a Literaturverz. S. 186 - 199 | ||
| 650 | 7 | |a Dickson, polynômes de |2 ram | |
| 650 | 7 | |a corps fini |2 inriac | |
| 650 | 7 | |a polynôme Dickson |2 inriac | |
| 650 | 4 | |a Dickson polynomials | |
| 650 | 0 | 7 | |a Dickson-Polynom |0 (DE-588)4366976-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dickson-Polynom |0 (DE-588)4366976-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Mullen, Gary L. |d 1947- |e Verfasser |0 (DE-588)123964059 |4 aut | |
| 700 | 1 | |a Turnwald, Gerhard |e Verfasser |4 aut | |
| 830 | 0 | |a Pitman monographs and surveys in pure and applied mathematics |v 65 |w (DE-604)BV000022446 |9 65 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006296183 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 266f 2001 A 22770 |
|---|---|
| DE-BY-TUM_katkey | 623143 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010415113 |
| _version_ | 1820800226119647232 |
| adam_text | Contents
PREFACE
CHAPTER 1. Algebraic Foundations 1
1. Polynomials 1
2. Finite Fields 3
3. The Ring of Integers mod m 4
4. Galois Rings 5
Exercises
Notes 7
CHAPTER 2. Basic Properties of Dickson Polynomials 8
1. Definition of Dickson Polynomials 8
2. Algebraic Properties 10
3. Analytic and Arithmetic Properties 15
4. Several Indeterminates 17
5. Other Related Polynomials and Functions 22
Exercises
Notes 34
CHAPTER 3. Finite Fields 38
1. Permutations 38
2. Factorization of Dn(x, a) 45
3. Value Sets 48
4. Fixed Points 54
5. Several Indeterminates 60
Exercises 73
Notes 75
CHAPTER 4. Integers mod m 79
1. Dickson Permutations 79
2. Fixed Points 88
3. Several Indeterminates 94
4. Redei Functions 99
Exercises 102
Contents
Notes 103
CHAPTER 5. Other Rings 105
1. Galois Rings 105
2. Infinite Algebraic Extensions of Finite Fields 116
3. Matrix Rings 118
Exercises 121
Notes 122
CHAPTER 6. The Schur Conjecture and its Converse 124
1. Prerequisites 124
2. Primitive Permutation Groups 125
3. The Galois Group of f(x) t over K{t) 128
4. Schur s Conjecture 131
5. Some Algebraic Number Theory 136
6. The Converse Problem 139
7. A Quantitative Refinement 146
Exercises 149
Notes 151
CHAPTER 7. Applications 155
1. Cryptology 155
2. Pseudoprimes 162
3. Permutation Polynomials and Complete Mappings 165
4. Dickson Polynomials and Irreducibles 172
5. Optimal Normal Bases 173
6. Character Sums 175
7. Combinatorial Applications 176
8. Circulant Determinants 177
Exercises 178
Notes 180
APPENDIX Tables of Dickson Polynomials 184
BIBLIOGRAPHY 186
LIST OF SYMBOLS 200
AUTHOR INDEX 202
SUBJECT INDEX 205
|
| any_adam_object | 1 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 230 |
| classification_tum | MAT 266f MAT 339f |
| ctrlnum | (OCoLC)26723766 (DE-599)BVBBV009534465 |
| dewey-full | 515/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 |
| dewey-search | 515/.55 |
| dewey-sort | 3515 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV009534465 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T13:19:52Z |
| institution | BVB |
| isbn | 0582091195 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006296183 |
| oclc_num | 26723766 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-12 DE-739 DE-29T DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-12 DE-739 DE-29T DE-11 |
| physical | 207 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Longman Scientific & Technical |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spellingShingle | Lidl, Rudolf 1948- Mullen, Gary L. 1947- Turnwald, Gerhard Dickson polynomials Pitman monographs and surveys in pure and applied mathematics Dickson, polynômes de ram corps fini inriac polynôme Dickson inriac Dickson polynomials Dickson-Polynom (DE-588)4366976-1 gnd |
| subject_GND | (DE-588)4366976-1 |
| title | Dickson polynomials |
| title_auth | Dickson polynomials |
| title_exact_search | Dickson polynomials |
| title_full | Dickson polynomials R. Lidl ; G. L. Mullen ; G. Turnwald |
| title_fullStr | Dickson polynomials R. Lidl ; G. L. Mullen ; G. Turnwald |
| title_full_unstemmed | Dickson polynomials R. Lidl ; G. L. Mullen ; G. Turnwald |
| title_short | Dickson polynomials |
| title_sort | dickson polynomials |
| topic | Dickson, polynômes de ram corps fini inriac polynôme Dickson inriac Dickson polynomials Dickson-Polynom (DE-588)4366976-1 gnd |
| topic_facet | Dickson, polynômes de corps fini polynôme Dickson Dickson polynomials Dickson-Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006296183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
| work_keys_str_mv | AT lidlrudolf dicksonpolynomials AT mullengaryl dicksonpolynomials AT turnwaldgerhard dicksonpolynomials |