Number theory with applications

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1. Verfasser: Li, Wen-Ching Winnie (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Singapore [u.a.] World Scientific 1998
Ausgabe:1. reprint
Schriftenreihe:Series on university mathematics 7
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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
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publishDate 1998
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publisher World Scientific
record_format marc
series Series on university mathematics
series2 Series on university mathematics
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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