Representation theory and automorphic forms:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2008
|
| Series: | Progress in mathematics
255 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 210 S. |
| ISBN: | 9780817645052 0817645055 9780817646462 |
Staff View
MARC
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| 245 | 1 | 0 | |a Representation theory and automorphic forms |c Toshiyuki Kobayashi ... ed. |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a VIII, 210 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 255 | |
| 650 | 4 | |a Darstellungstheorie - Automorphe Form - Kongress - Seoul <2005> | |
| 650 | 4 | |a Algebraic number theory | |
| 650 | 4 | |a Automorphic forms | |
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Record in the Search Index
| _version_ | 1804137152320110592 |
|---|---|
| adam_text | Contents
Preface
.........................................................
vii
1
Irreducibility and Cuspidality
Dinakar Ramakrishnan
............................................. 1
1
Preliminaries
................................................. 5
2
The first step in the proof
....................................... 15
3
The second step in the proof
.................................... 16
4
Galois representations attached to regular, selfdual cusp forms on GL(4)
18
5
Two useful lemmas on cusp forms on GL(4)
...................... 20
6
Finale
....................................................... 21
References
....................................................... 25
2
On Liftings of Holomorphic Modular Forms
Tamotsu Ikeda
.................................................... 29
1
Basic facts
................................................... 29
2
Fourier coefficients of the
Eisenstein
series
........................ 30
3
Kohnen plus space
............................................ 32
4
Lifting of cusp forms
.......................................... 33
5
Outline of the proof
........................................... 34
6
Relation to the Saito-Kurokawa lifts
............................. 35
7
Hermitian modular forms and hermitian Eisensetein series
........... 37
8
The case
m
-
In
+ 1.......................................... 39
9
The case
m
= 2n
............................................. 40
10
Ζ,
-functions
..................................................
40
11
The case
m
= 2............................................... 41
References
....................................................... 42
3
Multiplicity-free Theorems of the Restrictions of Unitary Highest
Weight Modules with respect to Reductive Symmetric Pairs
Toshiyuki Kobayashi
............................................... 45
vi
Contents
1
Introduction
and statement of main results
........................ 45
2
Main machinery from complex geometry
......................... 56
3
Proof of Theorem A
........................................... 61
4
Proof of Theorem
С
........................................... 68
5
Uniformly bounded multiplicities
—
Proof of Theorems
В
and
D
..... 70
6
Counterexamples
............................................. 77
7
Finite-dimensional cases
—
Proof of Theorems
E
and
F
............. 83
8
Generalization of the Hua-Kostant-Schmid formula
................ 89
9
Appendix: Associated bundles on Hermitian symmetric spaces
....... 103
References
....................................................... 105
4
The Rankin-Selberg Method for Automorphic Distributions
Stephen D. Miller and
Wilfried
Schmid
................................
Ill
1
Introduction
..................................................
Ill
2
Standard L-functions for SL(2)
................................. 115
3
Pairings of automorphic distributions
............................. 121
4
The Rankin-Selberg L-function for GL(2)
........................ 128
5
Exterior Square on GL(4)
...................................... 137
References
....................................................... 149
5 Langlands Functoriality
Conjecture and Number Theory
Freydoon Shahidi
................................................. 151
1
Introduction
.................................................. 151
2
Modular forms, Galois representations and
Artin
L-functions
........ 152
3
Lattice point problems and the Selberg conjecture
.................. 156
4
Ramanujan conjecture for Maass forms
........................... 158
5
Sato-Tate conjecture
.......................................... 159
6
Functoriality for symmetric powers
.............................. 161
7
Functoriality for classical groups
................................ 163
8
Ramanujan conjecture for classical groups
........................ 164
9
The method
.................................................. 166
References
....................................................... 169
6
Discriminant of Certain
К
3
Surfaces
Ken-lchi Yoshikawa
................................................ 175
1
Introduction
-
Discriminant of elliptic curves
...................... 175
2
КЗ
surfaces with involution and their moduli spaces
................ 178
3
Automorphic forms on the moduli space
.......................... 180
4
Equivariant analytic torsion and 2-elementary
КЗ
surfaces
........... 182
5
The Borcherds products
........................................ 184
6
Borcherds products for odd unimodular lattices
.................... 186
7
JO surfaces of Matsumoto-Sasaki-Yoshida
....................... 188
8
Discriminant of quartic surfaces
................................. 200
References
....................................................... 209
|
| adam_txt |
Contents
Preface
.
vii
1
Irreducibility and Cuspidality
Dinakar Ramakrishnan
. 1
1
Preliminaries
. 5
2
The first step in the proof
. 15
3
The second step in the proof
. 16
4
Galois representations attached to regular, selfdual cusp forms on GL(4)
18
5
Two useful lemmas on cusp forms on GL(4)
. 20
6
Finale
. 21
References
. 25
2
On Liftings of Holomorphic Modular Forms
Tamotsu Ikeda
. 29
1
Basic facts
. 29
2
Fourier coefficients of the
Eisenstein
series
. 30
3
Kohnen plus space
. 32
4
Lifting of cusp forms
. 33
5
Outline of the proof
. 34
6
Relation to the Saito-Kurokawa lifts
. 35
7
Hermitian modular forms and hermitian Eisensetein series
. 37
8
The case
m
-
In
+ 1. 39
9
The case
m
= 2n
. 40
10
Ζ,
-functions
.
40
11
The case
m
= 2. 41
References
. 42
3
Multiplicity-free Theorems of the Restrictions of Unitary Highest
Weight Modules with respect to Reductive Symmetric Pairs
Toshiyuki Kobayashi
. 45
vi
Contents
1
Introduction
and statement of main results
. 45
2
Main machinery from complex geometry
. 56
3
Proof of Theorem A
. 61
4
Proof of Theorem
С
. 68
5
Uniformly bounded multiplicities
—
Proof of Theorems
В
and
D
. 70
6
Counterexamples
. 77
7
Finite-dimensional cases
—
Proof of Theorems
E
and
F
. 83
8
Generalization of the Hua-Kostant-Schmid formula
. 89
9
Appendix: Associated bundles on Hermitian symmetric spaces
. 103
References
. 105
4
The Rankin-Selberg Method for Automorphic Distributions
Stephen D. Miller and
Wilfried
Schmid
.
Ill
1
Introduction
.
Ill
2
Standard L-functions for SL(2)
. 115
3
Pairings of automorphic distributions
. 121
4
The Rankin-Selberg L-function for GL(2)
. 128
5
Exterior Square on GL(4)
. 137
References
. 149
5 Langlands Functoriality
Conjecture and Number Theory
Freydoon Shahidi
. 151
1
Introduction
. 151
2
Modular forms, Galois representations and
Artin
L-functions
. 152
3
Lattice point problems and the Selberg conjecture
. 156
4
Ramanujan conjecture for Maass forms
. 158
5
Sato-Tate conjecture
. 159
6
Functoriality for symmetric powers
. 161
7
Functoriality for classical groups
. 163
8
Ramanujan conjecture for classical groups
. 164
9
The method
. 166
References
. 169
6
Discriminant of Certain
К
3
Surfaces
Ken-lchi Yoshikawa
. 175
1
Introduction
-
Discriminant of elliptic curves
. 175
2
КЗ
surfaces with involution and their moduli spaces
. 178
3
Automorphic forms on the moduli space
. 180
4
Equivariant analytic torsion and 2-elementary
КЗ
surfaces
. 182
5
The Borcherds products
. 184
6
Borcherds products for odd unimodular lattices
. 186
7
JO surfaces of Matsumoto-Sasaki-Yoshida
. 188
8
Discriminant of quartic surfaces
. 200
References
. 209 |
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| id | DE-604.BV022886224 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:52:01Z |
| indexdate | 2024-07-09T21:07:45Z |
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| physical | VIII, 210 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Representation theory and automorphic forms Toshiyuki Kobayashi ... ed. Boston [u.a.] Birkhäuser 2008 VIII, 210 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 255 Darstellungstheorie - Automorphe Form - Kongress - Seoul <2005> Algebraic number theory Automorphic forms Shimura varieties Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2005 Seoul gnd-content Darstellungstheorie (DE-588)4148816-7 s Automorphe Form (DE-588)4003972-9 s DE-604 Kobayashi, Toshiyuki 1962- Sonstige (DE-588)134051513 oth Progress in mathematics 255 (DE-604)BV000004120 255 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091134&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Representation theory and automorphic forms Progress in mathematics Darstellungstheorie - Automorphe Form - Kongress - Seoul <2005> Algebraic number theory Automorphic forms Shimura varieties Darstellungstheorie (DE-588)4148816-7 gnd Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4003972-9 (DE-588)1071861417 |
| title | Representation theory and automorphic forms |
| title_auth | Representation theory and automorphic forms |
| title_exact_search | Representation theory and automorphic forms |
| title_exact_search_txtP | Representation theory and automorphic forms |
| title_full | Representation theory and automorphic forms Toshiyuki Kobayashi ... ed. |
| title_fullStr | Representation theory and automorphic forms Toshiyuki Kobayashi ... ed. |
| title_full_unstemmed | Representation theory and automorphic forms Toshiyuki Kobayashi ... ed. |
| title_short | Representation theory and automorphic forms |
| title_sort | representation theory and automorphic forms |
| topic | Darstellungstheorie - Automorphe Form - Kongress - Seoul <2005> Algebraic number theory Automorphic forms Shimura varieties Darstellungstheorie (DE-588)4148816-7 gnd Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Darstellungstheorie - Automorphe Form - Kongress - Seoul <2005> Algebraic number theory Automorphic forms Shimura varieties Darstellungstheorie Automorphe Form Konferenzschrift 2005 Seoul |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091134&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT kobayashitoshiyuki representationtheoryandautomorphicforms |