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Bibliographic Details
Main Author:	Bruggeman, Roelof W. 1944- (Author)
Format:	Book
Language:	English
Published:	Basel u.a. Birkhäuser 1994
Series:	Monographs in mathematics 88
Subjects:	Formes automorphiques Automorphic forms Automorphe Form
Links:	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
Physical Description:	X, 317 S. graph. Darst.
ISBN:	3764350466 0817650466

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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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isbn	3764350466 0817650466
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physical	X, 317 S. graph. Darst.
publishDate	1994
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publisher	Birkhäuser
record_format	marc
series	Monographs in mathematics
series2	Monographs in mathematics
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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Call Number:	0102 MAT 103f 2001 A 8886 Floor plan
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