Number theory with applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1998
|
| Ausgabe: | 1. reprint |
| Schriftenreihe: | Series on university mathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 229 S. |
| ISBN: | 9810222262 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | WITH APPLICATIONS W. * WINNIE U DEPARTMENT OF MATHEMATICS PENNSYLVANIA
STATE UNIVERSITY |* WORLD SCIENTIFIC I SINGAPORE-NEW JERSEY LONDON
SINGAPORE * NEW JERSEY * LONDON * HONG KONG CONTENTS CHAPTER 1. FINITE
FIELDS §1. THE STRUCTURE OF A FINITE FIELD 1 §2. EXTENSIONS OF A FINITE
FIELD 3 §3. CHARACTERS 7 §4. CHARACTERS OF A FINITE FIELD, GAUSS SUMS 9
§5. DAVENPORT-HASSE IDENTITY 13 REFERENCES 16 CHAPTER 2. WEIL
CONJECTURES §1. NUMBERS OF SOLUTIONS OF EQUATIONS IN FINITE FIELDS 18
§2. WEIL CONJECTURES 21 §3. COHOMOLOGICAL INTERPRETATION OF THE WEIL
CONJECTURES 28 §4. ZETA FUNCTIONS AS EULER PRODUCTS 32 REFERENCES 34
CHAPTER 3. LOCAL AND GLOBAL FIELDS §1. LOCAL FIELDS 36 §2. EXTENSIONS OF
VALUATIONS 40 §3. ADELES AND IDELES 48 REFERENCES 54 CHAPTER 4. THE
RIEMANN-ROCH THEOREM §1. CHARACTERS OF A RESTRICTED PRODUCT 56 §2.
STANDARD ADDITIVE CHARACTERS 58 §3. DUALITY 62 §4. THE RIEMANN-ROCH
THEOREM 64 §5. COUNTING POINTS ON CURVES OVER FINITE FIELDS 68
REFERENCES 72 CHAPTER 5. ZETA AND L-FUNCTIONS §1. I-FUNCTIONS OF IDELE
CLASS CHARACTERS 73 IX X NUMBER THEORY WITH APPLICATIONS §2. FOURIER
TRANSFORMS 76 §3. ANALYTIC CONTINUATION AND FUNCTIONAL EQUATION FOR Z(S,
* *) 79 §4. THE ZETA FUNCTION OF * (A PROOF OF THEOREM 1) 83 §5. L(S, X)
FOR NONTRIVIAL X (A PROOF OF THEOREM 2) 87 REFERENCES 88 CHAPTER 6.
CHARACTER SUM ESTIMATES AND IDELE CLASS CHARACTERS §1. ROOTS OF
.//-FUNCTIONS 89 §2. A. WEIL S CHARACTER SUM ESTIMATES 93 §3. MORE
CHARACTER SUM ESTIMATES 103 §4. DAVENPORT-HASSE IDENTITY IN GENERAL FORM
109 §5. ZETA FUNCTIONS OF CERTAIN CURVES 113 REFERENCES 117 CHAPTER 7.
THE THEORY OF MODULAR FORMS §1. CLASSICAL MODULAR FORMS 118 §2. HECKE
OPERATORS 122 §3. THE STRUCTURE OF M(N, K,X) 128 §4. FUNCTIONAL
EQUATIONS 140 REFERENCES 149 CHAPTER 8. AUTOMORPHIC FORMS AND
AUTOMORPHIC REPRESENTATIONS §1. AUTOMORPHIC FORMS 152 §2.
REPRESENTATIONS OF GL2(F) FOR F A NONARCHIMEDEAN LOCAL FIELD 158 §3.
REPRESENTATIONS OF GL2(F) FOR F AN ARCHIMEDEAN LOCAL FIELD 170 §4.
AUTOMORPHIC REPRESENTATIONS OF GL 2 174 §5. REPRESENTATIONS OF
QUATERNION GROUPS 181 REFERENCES 186 CHAPTER 9. APPLICATIONS §1.
EXPANDERS, PROPERTY T AND EIGENVALUES 189 §2. SPECTRA OF REGULAR GRAPHS
192 §3. RAMANUJAN GRAPHS BASED ON QUATERNION GROUPS 195* §4. RAMANUJAN
GRAPHS BASED ON FINITE ABELIAN GROUPS 197 §5. RAMANUJAN GRAPHS BASED ON
FINITE NONABELIAN GROUPS 199 §6. TWO PROOFS OF THE ALON-BOPPANA THEOREM
207 §7. A LIMIT DISTRIBUTION 214 §8. THE GROWTH OF THE DIMENSION OF CUSP
FORMS WITH INTEGRAL EIGENVALUES AT P 216 REFERENCES 220 INDEX 223
|
| any_adam_object | 1 |
| author | Li, Wen-Ching Winnie |
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| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. reprint |
| format | Book |
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| id | DE-604.BV014093116 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:57:32Z |
| institution | BVB |
| isbn | 9810222262 |
| language | English |
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| physical | X, 229 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | World Scientific |
| record_format | marc |
| series | Series on university mathematics |
| series2 | Series on university mathematics |
| spelling | Li, Wen-Ching Winnie Verfasser aut Number theory with applications W. C. Winnie Li 1. reprint Singapore [u.a.] World Scientific 1998 X, 229 S. txt rdacontent n rdamedia nc rdacarrier Series on university mathematics 7 Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Series on university mathematics 7 (DE-604)BV008161912 7 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009654649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Wen-Ching Winnie Number theory with applications Series on university mathematics Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Number theory with applications |
| title_auth | Number theory with applications |
| title_exact_search | Number theory with applications |
| title_full | Number theory with applications W. C. Winnie Li |
| title_fullStr | Number theory with applications W. C. Winnie Li |
| title_full_unstemmed | Number theory with applications W. C. Winnie Li |
| title_short | Number theory with applications |
| title_sort | number theory with applications |
| topic | Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009654649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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