Spectral methods of automorphic forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2002
|
| Edition: | 2. ed. |
| Series: | Graduate studies in mathematics
53 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | First ed. published in Revista matemática iberoamericana in 1995 |
| Physical Description: | xi, 220 S. Ill. |
| ISBN: | 0821831607 9780821831601 |
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| 100 | 1 | |a Iwaniec, Henryk |d 1947- |e Verfasser |0 (DE-588)141817569 |4 aut | |
| 245 | 1 | 0 | |a Spectral methods of automorphic forms |c Henryk Iwaniec |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2002 | |
| 300 | |a xi, 220 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 53 | |
| 500 | |a First ed. published in Revista matemática iberoamericana in 1995 | ||
| 650 | 4 | |a Fonctions automorphes | |
| 650 | 4 | |a Formes automorphes | |
| 650 | 7 | |a Funções automorfas (funções de uma variável complexa) |2 larpcal | |
| 650 | 4 | |a Spectre (Mathématiques) | |
| 650 | 4 | |a Automorphic forms | |
| 650 | 4 | |a Automorphic functions | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
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| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Preface to the AMS Edition xi
Introduction 1
Chapter 0. Harmonic Analysis on the Euclidean Plane 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 15
1.4. Group decompositions 16
1.5. The classification of motions 17
1.6. The Laplace operator 19
1.7. Eigenfunctions of A 19
1.8. The invariant integral operators 26
1.9. The Green function on H 32
Chapter 2. Fuchsian Groups 37
2.1. Definitions 37
2.2. Fundamental domains 38
2.3. Basic examples 41
2.4. The double coset decomposition 45
v
vi Contents
2.5. Kloosterman sums 47
2.6. Basic estimates 49
Chapter 3. Automorphic Forms 53
3.1. Introduction 53
3.2. The Eisenstein series 56
3.3. Cusp forms 57
3.4. Fourier expansion of the Eisenstein series 59
Chapter 4. The Spectral Theorem. Discrete Part 63
4.1. The automorphic Laplacian 63
4.2. Invariant integral operators on C(r H) 64
4.3. Spectral resolution of A in C(T E) 68
Chapter 5. The Automorphic Green Function 71
5.1. Introduction 71
5.2. The Fourier expansion 72
5.3. An estimate for the automorphic Green function 75
5.4. Evaluation of some integrals 76
Chapter 6. Analytic Continuation of the Eisenstein Series 81
6.1. The Fredholm equation for the Eisenstein series 81
6.2. The analytic continuation of Ea(z, s) 84
6.3. The functional equations 86
6.4. Poles and residues of the Eisenstein series 88
Chapter 7. The Spectral Theorem. Continuous Part 95
7.1. The Eisenstein transform 96
7.2. Bessel s inequality 98
7.3. Spectral decomposition of £(r H) 101
7.4. Spectral expansion of automorphic kernels 104
Chapter 8. Estimates for the Fourier Coefficients of Maass Forms 107
8.1. Introduction 107
8.2. The Rankin Selberg L function 109
8.3. Bounds for linear forms 110
8.4. Spectral mean value estimates 113
Contents vii
8.5. The case of congruence groups 116
Chapter 9. Spectral Theory of Kloosterman Sums 121
9.1. Introduction 121
9.2. Analytic continuation of Zs(m, n) 122
9.3. Bruggeman Kuznetsov formula 125
9.4. Kloosterman sums formula 128
9.5. Petersson s formulas 131
Chapter 10. The Trace Formula 135
10.1. Introduction 135
10.2. Computing the spectral trace 139
10.3. Computing the trace for parabolic classes 142
10.4. Computing the trace for the identity motion 145
10.5. Computing the trace for hyperbolic classes 146
10.6. Computing the trace for elliptic classes 147
10.7. Trace formulas 150
10.8. The Selberg zeta function 152
10.9. Asymptotic law for the length of closed geodesies 154
Chapter 11. The Distribution of Eigenvalues 157
11.1. Weyl s law 157
11.2. The residual spectrum and the scattering matrix 162
11.3. Small eigenvalues 164
11.4. Density theorems 168
Chapter 12. Hyperbolic Lattice Point Problems 171
Chapter 13. Spectral Bounds for Cusp Forms 177
13.1. Introduction 177
13.2. Standard bounds 178
13.3. Applying the Hecke operator 180
13.4. Constructing an amplifier 181
13.5. The ergodicity conjecture 183
Appendix A. Classical Analysis 185
A.I. Self adjoint operators 185
viii Contents
A.2. Matrix analysis 187
A.3. The Hilbert Schmidt integral operators 189
A.4. The Fredholm integral equations 190
A.5. Green function of a differential equation 194
Appendix B. Special Functions 197
B.I. The gamma function 197
B.2. The hypergeometric functions 199
B.3. The Legendre functions 200
B.4. The Bessel functions 202
B.5. Inversion formulas 205
References 209
Subject Index 215
Notation Index 219
|
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| dewey-full | 511.3/3 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/3 |
| dewey-search | 511.3/3 |
| dewey-sort | 3511.3 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV014639493 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:36Z |
| institution | BVB |
| isbn | 0821831607 9780821831601 |
| language | English |
| lccn | 2002027749 |
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| physical | xi, 220 S. Ill. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Iwaniec, Henryk 1947- Verfasser (DE-588)141817569 aut Spectral methods of automorphic forms Henryk Iwaniec 2. ed. Providence, R.I. American Mathematical Society 2002 xi, 220 S. Ill. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 53 First ed. published in Revista matemática iberoamericana in 1995 Fonctions automorphes Formes automorphes Funções automorfas (funções de uma variável complexa) larpcal Spectre (Mathématiques) Automorphic forms Automorphic functions Spectral theory (Mathematics) Automorphe Funktion (DE-588)4143706-8 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Automorphe Funktion (DE-588)4143706-8 s Automorphe Form (DE-588)4003972-9 s Spektraltheorie (DE-588)4116561-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1798-7 Graduate studies in mathematics 53 (DE-604)BV009739289 53 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009942417&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iwaniec, Henryk 1947- Spectral methods of automorphic forms Graduate studies in mathematics Fonctions automorphes Formes automorphes Funções automorfas (funções de uma variável complexa) larpcal Spectre (Mathématiques) Automorphic forms Automorphic functions Spectral theory (Mathematics) Automorphe Funktion (DE-588)4143706-8 gnd Automorphe Form (DE-588)4003972-9 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4143706-8 (DE-588)4003972-9 (DE-588)4116561-5 |
| title | Spectral methods of automorphic forms |
| title_auth | Spectral methods of automorphic forms |
| title_exact_search | Spectral methods of automorphic forms |
| title_full | Spectral methods of automorphic forms Henryk Iwaniec |
| title_fullStr | Spectral methods of automorphic forms Henryk Iwaniec |
| title_full_unstemmed | Spectral methods of automorphic forms Henryk Iwaniec |
| title_short | Spectral methods of automorphic forms |
| title_sort | spectral methods of automorphic forms |
| topic | Fonctions automorphes Formes automorphes Funções automorfas (funções de uma variável complexa) larpcal Spectre (Mathématiques) Automorphic forms Automorphic functions Spectral theory (Mathematics) Automorphe Funktion (DE-588)4143706-8 gnd Automorphe Form (DE-588)4003972-9 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Fonctions automorphes Formes automorphes Funções automorfas (funções de uma variável complexa) Spectre (Mathématiques) Automorphic forms Automorphic functions Spectral theory (Mathematics) Automorphe Funktion Automorphe Form Spektraltheorie |
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