Introduction to the spectral theory of automorphic forms:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Madrid
Revista Matemática Iberoamericana
1995
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| Series: | Biblioteca de la revista matemática iberoamericana
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 247 S. graph. Darst. |
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| adam_text | INTRODUCTION TO THE SPECTRAL THEORY OF AUTOMORPHIC FORMS HENRYK IWANIEC
REVISTA MATEMATICA IBEROAMERICANA 1995 CONTENTS PREFACE INTRODUCTION
CHAPTER 0 HARMONIC ANALYSIS ON THE EUCLIDEAN PLANE XIII 1 3 CHAPTER 1
HARMONIC ANALYSIS ON THE HYPERBOLIC PLANE 7 1.1. THE UPPER HALF PLANE 7
1.2. H AS A HOMOGENEOUS SPACE 12 1.3. THE GEODESIC POLAR COORDINATES 16
1.4. BRUHAT DECOMPOSITION - 18 1.5. THE CLASSIFICATION OF MOTIONS 18
1.6. THE LAPLACE OPERATOR 20 1.7. EIGENFUNCTIONS OF A 21 1.8. THE
INVARIANT INTEGRAL OPERATORS 28 1.9. THE GREEN FUNCTION ON H 35 CHAPTER
2 FUCHSIAN GROUPS 39 2.1. DEFINITIONS 39 2.2. FUNDAMENTAL DOMAINS 41
2.3. BASIC EXAMPLES 44 2.4. THE DOUBLE COSET DECOMPOSITION 48 2.5.
KLOOSTERMAN SUMS 51 2.6. BASIC ESTIMATES 53 IX X CONTENTS CHAPTER 3
AUTOMORPHIC FORMS 57 3.1. INTRODUCTION 57 3.2. THE EISENSTEIN SERIES 61
3.3. CUSP FORMS 63 3.4. FOURIER EXPANSION OF THE EISENSTEIN SERIES 65
CHAPTER 4 THE SPECTRAL THEOREM. DISCRETE PART 69 4.1. THE AUTOMORPHIC
LAPLACIAN 69 4.2. INVARIANT INTEGRAL OPERATORS ON C(F H) 70 4.3.
SPECTRAL RESOLUTION OF A IN C(R H) 75 CHAPTER 5 THE AUTOMORPHIC GREEN
FUNCTION 77 5.1. INTRODUCTION 77 5.2. THE FOURIER EXPANSION 78 5.3. AN
ESTIMATE FOR THE AUTOMORPHIC GREEN FUNCTION 81 5.4. EVALUATION OF SOME
INTEGRALS 83 CHAPTER 6 ANALYTIC CONTINUATION OF THE EISENSTEIN SERIES 87
6.1. THE FREDHOLM EQUATION FOR THE EISENSTEIN SERIES 87 6.2. THE
ANALYTIC CONTINUATION OF E A (Z,S) 90 6.3. THE FUNCTIONAL EQUATIONS 93
6.4. POLES AND RESIDUES OF THE EISENSTEIN SERIES 95 CHAPTER 7 THE
SPECTRAL THEOREM. CONTINUOUS PART 103 7.1. THE EISENSTEIN TRANSFORM 104
7.2. BESSEL S INEQUALITY 107 7.3. SPECTRAL DECOMPOSITION OF (R H) 110
7.4. SPECTRAL EXPANSION OF AUTOMORPHIC KERNELS 113 CONTENTS XI CHAPTER 8
ESTIMATES FOR THE FOURIER COEFFICIENTS OF MAASS FORMS 117 8.1.
INTRODUCTION 117 8.2. THE RANKIN-SELBERG CONVOLUTION 119 8.3. BOUNDS FOR
LINEAR FORMS 121 8.4. SPECTRAL MEAN-VALUE ESTIMATES 123 8.5. THE CASE OF
CONGRUENCE GROUPS 126 CHAPTER 9 SPECTRAL THEORY OF KLOOSTERMAN SUMS 133
9.1. INTRODUCTION 133 9.2. ANALYTIC CONTINUATION OF Z S (M,N) 134 9.3.
BRUGGEMAN-KUZNETSOV FORMULA 138 9.4. BRUGGEMAN-KUZNETSOV FORMULA
REVERSED 141 9.5. PETERSSON S FORMULAS 144 CHAPTER 10 THE TRACE FORMULA
149 10.1. INTRODUCTION 149 10.2. COMPUTING THE SPECTRAL TRACE 154 10.3.
COMPUTING THE TRACE FOR PARABOLIC CLASSES 157 10.4. COMPUTING THE TRACE
FOR THE IDENTITY MOTION 161 10.5. COMPUTING THE TRACE FOR HYPERBOLIC
CLASSES 161 10.6. COMPUTING THE TRACE FOR ELLIPTIC CLASSES V 163 10.7.
TRACE FORMULAS 166 10.8. THE SELBERG ZETA-FUNCTION 168 10.9. ASYMPTOTIC
LAW FOR THE LENGTH OF CLOSED GEODESIES 170 CHAPTER 11 THE DISTRIBUTION
OF EIGENVALUES 173 11.1. WEYL S LAW 173 11.2. THE RESIDUAL SPECTRUM AND
THE SCATTERING MATRIX 179 11.3. SMALL EIGENVALUES 181 11.4. DENSITY
THEOREMS 185 XII CONTENTS CHAPTER 12 HYPERBOLIC LATTICE-POINT PROBLEMS
189 CHAPTER 13 SPECTRAL BOUNDS FOR CUSP FORMS 195 13.1. INTRODUCTION 195
13.2. STANDARD BOUNDS 196 13.3. APPLYING THE HECKE OPERATOR 198 13.4.
CONSTRUCTING AN AMPLIFIER 200 13.5. THE UNIQUE ERGODICITY CONJECTURE 202
APPENDIX A CLASSICAL ANALYSIS 205 A.I. SELF-ADJOINT OPERATORS 205 A.2.
MATRIX ANALYSIS 208 A.3. THE HILBERT-SCHMIDT INTEGRAL OPERATORS 209 A.4.
THE FREDHOLM INTEGRAL OPERATORS 210 A.5. GREEN FUNCTION OF A
DIFFERENTIAL EQUATION 215 APPENDIX B SPECIAL FUNCTIONS 219 B.I. THE
GAMMA FUNCTION 219 B.2. THE HYPERGEOMETRIC FUNCTIONS 221 B.3. THE
LEGENDRE FUNCTIONS 223 B.4. THE BESSEL FUNCTIONS 224 B.5. INVERSION
FORMULAS 228 REFERENCES SUBJECT INDEX NOTATION INDEX 233 239 245
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512.7 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T17:48:12Z |
| institution | BVB |
| language | English |
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| physical | XIII, 247 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Revista Matemática Iberoamericana |
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| spelling | Iwaniec, Henryk Verfasser aut Introduction to the spectral theory of automorphic forms Henryk Iwaniec Madrid Revista Matemática Iberoamericana 1995 XIII, 247 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Biblioteca de la revista matemática iberoamericana Automorphic forms Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s Spektraltheorie (DE-588)4116561-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006773599&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iwaniec, Henryk Introduction to the spectral theory of automorphic forms Automorphic forms Spektraltheorie (DE-588)4116561-5 gnd Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4003972-9 |
| title | Introduction to the spectral theory of automorphic forms |
| title_auth | Introduction to the spectral theory of automorphic forms |
| title_exact_search | Introduction to the spectral theory of automorphic forms |
| title_full | Introduction to the spectral theory of automorphic forms Henryk Iwaniec |
| title_fullStr | Introduction to the spectral theory of automorphic forms Henryk Iwaniec |
| title_full_unstemmed | Introduction to the spectral theory of automorphic forms Henryk Iwaniec |
| title_short | Introduction to the spectral theory of automorphic forms |
| title_sort | introduction to the spectral theory of automorphic forms |
| topic | Automorphic forms Spektraltheorie (DE-588)4116561-5 gnd Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Automorphic forms Spektraltheorie Automorphe Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006773599&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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