Elementary number theory, group theory, and Ramanujan graphs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society student texts
55 |
| Subjects: | |
| Online Access: | Sample text Publisher description Table of contents Inhaltsverzeichnis |
| Physical Description: | VIII, 144 S. Ill. |
| ISBN: | 0521824265 0521531438 |
Staff View
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| 245 | 1 | 0 | |a Elementary number theory, group theory, and Ramanujan graphs |c Guiliana Davidoff ; Peter Sarnak ; Alain Valette |
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Record in the Search Index
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| adam_text | Contents
Preface page ix
An Overview 1
Chapter 1. Graph Theory 8
1.1. The Adjacency Matrix and Its Spectrum 8
1.2. Inequalities on the Spectral Gap 12
1.3. Asymptotic Behavior of Eigenvalues in Families
of Expanders 18
1.4. Proof of the Asymptotic Behavior 20
1.5. Independence Number and Chromatic Number 30
1.6. Large Girth and Large Chromatic Number 32
1.7. Notes on Chapter 1 36
Chapter 2. Number Theory 38
2.1. Introduction 38
2.2. Sums of Two Squares 39
2.3. Quadratic Reciprocity 48
2.4. Sums of Four Squares 52
2.5. Quaternions 57
2.6. The Arithmetic of Integer Quaternions 59
2.7. Notes on Chapter 2 70
Chapters PSL2(tf) 72
3.1. Some Finite Groups 72
3.2. Simplicity 73
3.3. Structure of Subgroups 76
3.4. Representation Theory of Finite Groups 85
3.5. Degrees of Representations of PSL2(tf) 102
3.6. Notes on Chapter 3 107
Chapter 4. The Graphs X™ 108
4.1. Cay ley Graphs 108
4.2. Construction of X 1 112
4.3. Girth and Connectedness 115
4.4. Spectral Estimates 122
4.5. Notes on Chapter 4 130
Appendix 4. Regular Graphs with Large Girth 132
Bibliography 138
Index 143
|
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| language | English |
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| physical | VIII, 144 S. Ill. |
| publishDate | 2003 |
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| publisher | Cambridge Univ. Press |
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| spelling | Davidoff, Giuliana P. Verfasser (DE-588)1029583447 aut Elementary number theory, group theory, and Ramanujan graphs Guiliana Davidoff ; Peter Sarnak ; Alain Valette 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2003 VIII, 144 S. Ill. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society student texts 55 Graph theory Group theory Number theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Gruppentheorie (DE-588)4072157-7 s Sarnak, Peter 1953- Sonstige (DE-588)102958365X oth Valette, Alain ca. 1890 Sonstige (DE-588)123654734 oth London Mathematical Society: London Mathematical Society student texts 55 (DE-604)BV000841726 55 http://www.loc.gov/catdir/samples/cam034/2002074057.html Sample text http://www.loc.gov/catdir/description/cam031/2002074057.html Publisher description http://www.loc.gov/catdir/toc/cam031/2002074057.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940613&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davidoff, Giuliana P. Elementary number theory, group theory, and Ramanujan graphs London Mathematical Society: London Mathematical Society student texts Graph theory Group theory Number theory Gruppentheorie (DE-588)4072157-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4067277-3 |
| title | Elementary number theory, group theory, and Ramanujan graphs |
| title_auth | Elementary number theory, group theory, and Ramanujan graphs |
| title_exact_search | Elementary number theory, group theory, and Ramanujan graphs |
| title_full | Elementary number theory, group theory, and Ramanujan graphs Guiliana Davidoff ; Peter Sarnak ; Alain Valette |
| title_fullStr | Elementary number theory, group theory, and Ramanujan graphs Guiliana Davidoff ; Peter Sarnak ; Alain Valette |
| title_full_unstemmed | Elementary number theory, group theory, and Ramanujan graphs Guiliana Davidoff ; Peter Sarnak ; Alain Valette |
| title_short | Elementary number theory, group theory, and Ramanujan graphs |
| title_sort | elementary number theory group theory and ramanujan graphs |
| topic | Graph theory Group theory Number theory Gruppentheorie (DE-588)4072157-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Graph theory Group theory Number theory Gruppentheorie Zahlentheorie |
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