Families of automorphic forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1994
|
| Series: | Monographs in mathematics
88 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 317 S. graph. Darst. |
| ISBN: | 3764350466 0817650466 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface IX
1 Modular introduction
1.1 The modular group 1
1.2 Maass forms 3
1.3 Holomorphic modular forms 5
1.4 Fourier expansion 7
1.5 More modular forms 9
1.6 Truncation and perturbation 14
1.7 Further remarks 18
1 General theory
2 Universal covering group
2.1 Upper half plane 25
2.2 Universal covering group 27
2.3 Automorphic forms 31
3 Discrete subgroups
3.1 Cofinite groups 33
3.2 The quotient 35
3.3 Canonical generators 37
3.4 Characters 42
3.5 Notations 44
4 Automorphic forms
4.1 Fourier expansion 48
4.2 Spaces of Fourier terms 51
4.3 Growth condition 58
4.4 Differentiation of Fourier terms 61
4.5 Differentiation of automorphic forms 65
4.6 Maass Selberg relation 66
5 Poincare series
5.1 Construction of Poincare series 71
5.2 Fourier coefficients 78
V
VI Contents
6 Selfadjoint extension
6.1 Hilbert space 86
6.2 Energy subspace 88
6.3 Fourier coefficients 91
6.4 Compactness 94
6.5 Extension of the Casimir operator 97
6.6 Relation to automorphic forms 99
6.7 The discrete spectrum 101
7 Families of automorphic forms
7.1 Parameter spaces 107
7.2 Holomorphic families 109
7.3 Families of eigenfunctions 113
7.4 Automorphic transformation behavior 117
7.5 Families of automorphic forms 123
7.6 Families of Fourier terms 124
7.7 Differentiation 130
8 Transformation and truncation
8.1 Parameter space 133
8.2 Transformation 135
8.3 Truncation 138
8.4 Energy subspace 141
8.5 Families of automorphic forms 147
9 Pseudo Casimir operator
9.1 Sesquilinear form 151
9.2 Pseudo Casimir operator 156
9.3 Meromorphy of the resolvent 160
9.4 Meromorphic families 167
9.5 Dimension 174
10 Meromorphic continuation
10.1 Cells of continuation 177
10.2 Meromorphic continuation 180
10.3 Functional equations 185
11 Poincare families along vertical lines
11.1 General results 191
11.2 Eisenstein families 198
11.3 Other Poincare families 203
Contents VII
12 Singularities of Poincare families
12.1 Local curves 213
12.2 Value sets 217
12.3 General results 221
12.4 General parameter spaces 227
12.5 Restricted parameter spaces 230
II Examples
13 Modular group
13.1 The covering group 239
13.2 Fourier expansions 244
13.3 The modular spectrum 247
13.4 Families of modular forms 249
13.5 Derivatives 252
13.6 Distribution results 258
14 Theta group
14.1 Theta group 265
14.2 The covering group 266
14.3 Fourier expansions 268
14.4 Eisenstein series 271
14.5 More than one parameter 274
15 Commutator subgroup
15.1 Commutator subgroup 275
15.2 Automorphic forms 278
15.3 The period map 280
15.4 Poincare series 284
15.5 Eisenstein family of weight 0 286
15.6 Harmonic automorphic forms 290
15.7 Maass forms 302
References 307
Index 311
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:58Z |
| institution | BVB |
| isbn | 3764350466 0817650466 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006396557 |
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| physical | X, 317 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Bruggeman, Roelof W. 1944- Verfasser (DE-588)109761758 aut Families of automorphic forms Roelof W. Bruggeman Basel u.a. Birkhäuser 1994 X, 317 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 88 Formes automorphiques ram Automorphic forms Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s DE-604 Monographs in mathematics 88 (DE-604)BV000008284 88 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006396557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bruggeman, Roelof W. 1944- Families of automorphic forms Monographs in mathematics Formes automorphiques ram Automorphic forms Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4003972-9 |
| title | Families of automorphic forms |
| title_auth | Families of automorphic forms |
| title_exact_search | Families of automorphic forms |
| title_full | Families of automorphic forms Roelof W. Bruggeman |
| title_fullStr | Families of automorphic forms Roelof W. Bruggeman |
| title_full_unstemmed | Families of automorphic forms Roelof W. Bruggeman |
| title_short | Families of automorphic forms |
| title_sort | families of automorphic forms |
| topic | Formes automorphiques ram Automorphic forms Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Formes automorphiques Automorphic forms Automorphe Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006396557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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