The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Kingston, Ontario
Queen's Univ.
1993
|
| Series: | Queen's papers in pure and applied mathematics
93 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 181 S. |
| ISBN: | 0889116369 |
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| 245 | 1 | 0 | |a The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem |c by Vijay Jha |
| 264 | 1 | |a Kingston, Ontario |b Queen's Univ. |c 1993 | |
| 300 | |a XIV, 181 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Queen's papers in pure and applied mathematics |v 93 | |
| 650 | 7 | |a Fermat, Grand théorème de |2 ram | |
| 650 | 4 | |a Idéal Stickel-Berger | |
| 650 | 4 | |a Irrégularité nombre premier | |
| 650 | 4 | |a Matrice Carlitz | |
| 650 | 4 | |a Nombre Bernouilli | |
| 650 | 4 | |a Nombre classe | |
| 650 | 4 | |a Q(zêta-p) | |
| 650 | 4 | |a Somme Jacobi | |
| 650 | 4 | |a Théorie Kummer | |
| 650 | 4 | |a Théorème Fermat | |
| 650 | 4 | |a Théorème Krasner | |
| 650 | 4 | |a Théorème Sophie Germain | |
| 650 | 4 | |a Class groups (Mathematics) | |
| 650 | 4 | |a Fermat's last theorem | |
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| 650 | 0 | 7 | |a Stickelberger-Ideal |0 (DE-588)4325817-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804122544249241600 |
|---|---|
| adam_text | CONTENTS
PREFACE iv
LIST OF SYMBOLS xi
CHAPTER 1
Rummer s basis of the Stickelberger Ideal, the Carlitz Matrix
and the Structure of the Class group 1
0. Preliminaries 5
1. Kummer s basis of the Stickelberger ideal 10
2. Applications to the structure of the class group 14
3. Appendix 17
CHAPTER 2
On the Irregularity of a Prime 20
0. Preliminaries 23
1. Irregularity and the Stickelberger Ideal 26
2. The Index of Irregularity and the Stickelberger Ideal 33
CHAPTER 3
Identities in the Stickelberger Ideal and Summation
Criteria for Bernoulli Numbers and Fermat s Last Theorem 38
0. Preliminaries 42
1. Identities in the Stickelberger ideal 45
2. Summation criteria for Bernoulli numbers 53
3. Congruences for Bernoulli numbers with
least possible number of summands 58
4. Summation Criterion for the
first Case of Fermat s Last Theorem 62
CHAPTER 4
Some Class Number Formulae for the Imaginary Subfields
of Q( ) 67
p
0. Preliminaries 71
1. Class number formulae for Imaginary Subfields of 0( ; ) 72
2. Class number formulae for OCv p), p = 3 (mod 4) 75
3. The Class number of Q(v p), p = 3 (mod 4) and the
Exponent of ST/3~ 78
4. Class number formulae for Quartic Subfields of 0( ),
p
p s 5 (mod 8) 79
CHAPTER 5
Some Remarks on Jacob! sums 82
0. Preliminaries 84
1. The Stickelberger Ideal and Jacobi Sums 88
ii
2. Identities for Jacobi Sums 96
CHAPTER 6
The Stickelberger Ideal and Proper Imaginary Subfields
of Q( ) 102
p
0. Preliminaries 105
1. The Order of K /3 and the Class number of R 107
e e e
2. The Carlitz matrix for R 112
e
3. Applications to the Structure of the Class group of % 113
4. On Imaginary Quartic subfield of Q( ) 116
p
CHAPTER 7
On Rummer s theory for the first case OF
Fermat s Last Theorem 120
0. Preliminaries 123
1. The Stickelberger ideal and Kummer s congruences 126
2. The Stickelberger ideal and Mirimonoff s congruences 133
CHAPTER 8
Faster computation of some invariants of Q(£ ) 141
p
1. Faster computation of irregular pairs 146
2. Faster computation of the first factor of
class number of Q(C ) 148
p
CHAPTER 9
On Krasner s Theorem for the first case of
Fermat s Last Theorem 155
1. The best possible bounds 158
2. Proof of the Theorem 161
CHAPTER 10
On Sophie Germain s Theorem for the first case of
Fermat s Last Theorem 169
REFERENCES 174
iii
|
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| author_facet | Jha, Vijay |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV008162263 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:15:34Z |
| institution | BVB |
| isbn | 0889116369 |
| language | English |
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| physical | XIV, 181 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Queen's Univ. |
| record_format | marc |
| series | Queen's papers in pure and applied mathematics |
| series2 | Queen's papers in pure and applied mathematics |
| spelling | Jha, Vijay Verfasser aut The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem by Vijay Jha Kingston, Ontario Queen's Univ. 1993 XIV, 181 S. txt rdacontent n rdamedia nc rdacarrier Queen's papers in pure and applied mathematics 93 Fermat, Grand théorème de ram Idéal Stickel-Berger Irrégularité nombre premier Matrice Carlitz Nombre Bernouilli Nombre classe Q(zêta-p) Somme Jacobi Théorie Kummer Théorème Fermat Théorème Krasner Théorème Sophie Germain Class groups (Mathematics) Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd rswk-swf Stickelberger-Ideal (DE-588)4325817-7 gnd rswk-swf Stickelberger-Ideal (DE-588)4325817-7 s Fermatsche Vermutung (DE-588)4154012-8 s DE-604 Queen's papers in pure and applied mathematics 93 (DE-604)BV001889470 93 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005385035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jha, Vijay The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem Queen's papers in pure and applied mathematics Fermat, Grand théorème de ram Idéal Stickel-Berger Irrégularité nombre premier Matrice Carlitz Nombre Bernouilli Nombre classe Q(zêta-p) Somme Jacobi Théorie Kummer Théorème Fermat Théorème Krasner Théorème Sophie Germain Class groups (Mathematics) Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd Stickelberger-Ideal (DE-588)4325817-7 gnd |
| subject_GND | (DE-588)4154012-8 (DE-588)4325817-7 |
| title | The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem |
| title_auth | The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem |
| title_exact_search | The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem |
| title_full | The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem by Vijay Jha |
| title_fullStr | The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem by Vijay Jha |
| title_full_unstemmed | The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem by Vijay Jha |
| title_short | The Stickelberger ideal in the spirit of Kummer with application to the first case of Fermat's last theorem |
| title_sort | the stickelberger ideal in the spirit of kummer with application to the first case of fermat s last theorem |
| topic | Fermat, Grand théorème de ram Idéal Stickel-Berger Irrégularité nombre premier Matrice Carlitz Nombre Bernouilli Nombre classe Q(zêta-p) Somme Jacobi Théorie Kummer Théorème Fermat Théorème Krasner Théorème Sophie Germain Class groups (Mathematics) Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd Stickelberger-Ideal (DE-588)4325817-7 gnd |
| topic_facet | Fermat, Grand théorème de Idéal Stickel-Berger Irrégularité nombre premier Matrice Carlitz Nombre Bernouilli Nombre classe Q(zêta-p) Somme Jacobi Théorie Kummer Théorème Fermat Théorème Krasner Théorème Sophie Germain Class groups (Mathematics) Fermat's last theorem Fermatsche Vermutung Stickelberger-Ideal |
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