Automorphic forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2013
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Dt. |
| Physical Description: | IX, 252 S. graph. Darst. |
| ISBN: | 9781447144342 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804149599278989313 |
|---|---|
| adam_text | Contents
1 Doubly Periodic Functions............................................ 1
1.1 Definition and First Properties................................. 1
1.2 The p-Function of Weierstrass................................... 4
1.3 The Differential Equation of the p-Function..................... 7
1.4 Eisenstein Series............................................... 8
1.5 Bernoulli Numbers and Values of the Zeta Function............... 9
1.6 Exercises and Remarks ......................................... 11
2 Modular Forms for SL^iZ) ........................................... 15
2.1 The Modular Group.............................................. 15
2.2 Modular Forms.................................................. 20
2.3 Estimating Fourier Coefficients................................ 30
2.4 L-Functions.................................................... 31
2.5 Hecke Operators................................................ 37
2.6 Congruence Subgroups........................................... 51
2.7 Non-holomorphic Eisenstein Series.............................. 53
2.8 MaaB Wave Forms................................................ 63
2.9 Exercises and Remarks ......................................... 73
3 Representations of SL2(R)........................................... 79
3.1 Haar Measures and Decompositions............................... 79
3.1.1 The Modular Function.................................... 84
3.2 Representations................................................ 87
3.3 Modular Forms as Representation Vectors ....................... 92
3.4 The Exponential Map............................................ 97
3.5 Exercises and Remarks .........................................100
4 /?-A die Numbers....................................................105
4.1 Absolute Values.............................................. 105
4.2 Qp as Completion of Q..........................................107
4.3 Power Series...................................................109
4.4 Haar Measures..................................................112
vii
viii Contents
4.5 Direct and Projective Limits....................................115
4.6 Exercises.......................................................120
5 Adeles and Ideles.....................................................123
5.1 Restricted Products ............................................123
5.2 Adeles..........................................................125
5.3 Ideles..........................................................128
5.4 Fourier Analysis on A...........................................131
5.4.1 Local Fourier Analysis ..................................134
5.4.2 Global Fourier Analysis..................................136
5.5 Exercises.......................................................139
6 Tate’s Thesis ........................................................143
6.1 Poisson Summation Formula and the Riemann Zeta Function ... 143
6.2 Zeta Functions in the Adelic Setting............................145
6.3 Dirichlet L-Functions...........................................150
6.4 Galois Representations and L-Functions..........................156
6.5 Exercises.......................................................160
7 Automorphic Representations of GL2( A).............................163
7.1 Principal Series Representations................................163
7.2 From Real to Adelic.............................................168
7.3 Bochner Integral. Compact Operators and Arzela-Ascoli ..........172
7.3.1 The Arzela-Ascoli Theorem................................180
7.4 Cusp Forms .....................................................182
7.5 The Tensor Product Theorem......................................185
7.5.1 Synthesis................................................185
7.5.2 Analysis.................................................193
7.5.3 Admissibility of Automorphic Representations.............205
7.6 Exercises and Remarks ..........................................206
8 Automorphic L-Functions............................................211
8.1 The Lattice M2(Q)...............................................211
8.2 Local Factors...................................................212
8.3 Global L-Functions..............................................224
8.4 The Example of Classical Cusp Forms.............................235
8.5 Exercises and Remarks ..........................................238
Appendix Measure and Integration...........................................241
A.l Measurable Functions and Integration............................241
A.2 Fubini s Theorem................................................243
A.3 ¿¿’-Spaces......................................................245
References.................................................................247
Index......................................................................249
|
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| bvnumber | BV040517120 |
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| indexdate | 2024-07-10T00:25:33Z |
| institution | BVB |
| isbn | 9781447144342 |
| language | English |
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| physical | IX, 252 S. graph. Darst. |
| publishDate | 2013 |
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| spelling | Deitmar, Anton 1960- Verfasser (DE-588)103439682X aut Automorphe Formen Automorphic forms Anton Deitmar London [u.a.] Springer 2013 IX, 252 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Aus dem Dt. Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4471-4435-9 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025363504&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Deitmar, Anton 1960- Automorphic forms Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4003972-9 |
| title | Automorphic forms |
| title_alt | Automorphe Formen |
| title_auth | Automorphic forms |
| title_exact_search | Automorphic forms |
| title_full | Automorphic forms Anton Deitmar |
| title_fullStr | Automorphic forms Anton Deitmar |
| title_full_unstemmed | Automorphic forms Anton Deitmar |
| title_short | Automorphic forms |
| title_sort | automorphic forms |
| topic | Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Automorphe Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025363504&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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