Groups acting on hyperbolic space: harmonic analysis and number theory
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1997
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 497 - 520 |
| Beschreibung: | XV, 524 S. graph. Darst. |
| ISBN: | 3540627456 |
Internformat
MARC
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| 100 | 1 | |a Elstrodt, Jürgen |d 1940- |e Verfasser |0 (DE-588)11570597X |4 aut | |
| 245 | 1 | 0 | |a Groups acting on hyperbolic space |b harmonic analysis and number theory |c J. Elstrodt ; F. Grunewald ; J. Mennicke |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
| 300 | |a XV, 524 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Literaturverz. S. 497 - 520 | ||
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 4 | |a Selberg trace formula | |
| 650 | 4 | |a Automorphic forms | |
| 650 | 4 | |a Functions, Zeta | |
| 650 | 0 | 7 | |a Automorphe Funktion |0 (DE-588)4143706-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gruppenoperation |0 (DE-588)4158467-3 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Mennicke, Jens |d 1931- |e Verfasser |0 (DE-588)115706062 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1807865291148886016 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
PREFACE
.
VII
1.
THREE-DIMENSIONAL
HYPERBOLIC
SPACE
.
1
1.1
THE
UPPER
HALF-SPACE
MODEL
.
1
1.2
THE
UNIT
BALL
MODEL
.
9
1.3
THE
EXCEPTIONAL
ISOMORPHISM
.
12
1.4
THE
HYPERBOLOID
MODEL
.
20
1.5
THE
KLEINIAN
MODEL
.
22
1.6
UPPER
HALF-SPACE
AS
A
SYMMETRIC
SPACE
.
28
1.7
NOTES
AND
REMARKS
.
30
2.
GROUPS
ACTING
DISCONTINUOUSLY
ON
THREE-DIMENSIONAL
HYPERBOLIC
SPACE
.
33
2.1
DISCONTINUITY
.
33
2.2
FUNDAMENTAL
DOMAINS
AND
POLYHEDRA
.
41
2.3
SHIMIZU
'
S
LEMMA
.
48
2.4
JORGENSEN
'
S
INEQUALITY
.
53
2.5
COVOLUMES
.
59
2.6
HYPERBOLIC
LATTICE
POINT
PROBLEMS
.
67
2.7
GENERATORS
AND
RELATIONS
.
71
2.8
CONJUGACY
AND
COMMENSURABILITY
.
75
2.9
A
LEMMA
OF
SELBERG
.
78
2.10
NOTES
AND
REMARKS
.
80
3.
AUTOMORPHIC
FUNCTIONS
.
83
3.1
DEFINITION
AND
ELEMENTARY
PROPERTIES
OF
SOME
POINCARE
SERIES
.
84
3.2
DEFINITION
AND
ELEMENTARY
PROPERTIES
OF
EISENSTEIN
SERIES
.
98
3.3
FOURIER
EXPANSION
IN
CUSPS
AND
THE
MAAB-SELBERG
RELATIONS
.
105
3.4
FOURIER
EXPANSION
OF
EISENSTEIN
SERIES
.
110
3.5
EXPANSION
OF
EIGENFUNCTIONS
AND
THE
SELBERG
TRANSFORM
.
114
3.6
BEHAVIOUR
OF
THE
POINCARE
SERIES
AT
THE
ABSCISSA
OF
CONVERGENCE
.
122
3.7
NOTES
AND
REMARKS
.
129
XIV
TABLE
OF
CONTENTS
4.
SPECTRAL
THEORY
OF
THE
LAPLACE
OPERATOR
.
131
4.1
ESSENTIAL
SELF-ADJOINTNESS
OF
THE
LAPLACE-BELTRAMI
OPERATOR
.
132
4.2
THE
RESOLVENT
KERNEL
.
143
4.3
HILBERT-SCHMIDT
TYPE
RESOLVENTS
.
156
4.4
ANALYTIC
CONTINUATION
OF
THE
RESOLVENT
KERNEL
.
162
4.5
APPROXIMATION
BY
KERNELS
OF
HILBERT-SCHMIDT
TYPE
.
169
5.
SPECTRAL
THEORY
OF
THE
LAPLACE
OPERATOR
FOR
COCOMPACT
GROUPS
.
185
5.1
THE
HYPERBOLIC
LATTICE-POINT
PROBLEM
.
187
5.2
COMPUTATION
OF
THE
TRACE
.
190
5.3
HUBER
'
S
THEOREM
.
201
5.4
THE
SELBERG
ZETA
FUNCTION
.
205
5.5
WEYL
'
S
ASYMPTOTIC
LAW
AND
THE
HADAMARD
FACTORISATION
OF
THE
ZETA
FUNCTION
.
210
5.6
ANALOGUE
OF
THE
LINDELOF
HYPOTHESIS
FOR
THE
SELBERG
ZETA
FUNCTION
.
218
5.7
THE
PRIME
GEODESIC
THEOREM
.
222
5.8
NOTES
AND
REMARKS
.
228
6.
SPECTRAL
THEORY
OF
THE
LAPLACE
OPERATOR
FOR
COFINITE
GROUPS
.
231
6.1
MEROMORPHIC
CONTINUATION
OF
THE
EISENSTEIN
SERIES
.
231
6.2
GENERALITIES
ON
EIGENFUNCTIONS
AND
EIGENPACKETS
.
244
6.3
SPECTRAL
DECOMPOSITION
THEORY
.
265
6.4
SPECTRAL
EXPANSIONS
OF
INTEGRAL
KERNELS
AND
POINCARE
SERIES
.
276
6.5
THE
TRACE
FORMULA
AND
SOME
APPLICATIONS
.
296
6.6
NOTES
AND
REMARKS
.
310
7.
PSL(2)
OVER
RINGS
OF
IMAGINARY
QUADRATIC
INTEGERS
.
311
7.1
INTRODUCTION
OF
THE
GROUPS
.
311
7.2
THE
CUSPS
.
313
7.3
DESCRIPTION
OF
A
FUNDAMENTAL
DOMAIN
.
318
7.4
GROUPS
COMMENSURABLE
WITH
PSL(2,
0)
.
327
7.5
THE
GROUP
THEORETIC
STRUCTURE
OF
PSL(2,
O)
.
334
7.6
SPECTRAL
THEORY
OF
THE
LAPLACE
OPERATOR
.
346
7.7
NOTES
AND
REMARKS
.
356
8.
EISENSTEIN
SERIES
FOR
PSL(2)
OVER
IMAGINARY
QUADRATIC
INTEGERS
.
359
8.1
FUNCTIONS
CLOSELY
RELATED
TO
EISENSTEIN
SERIES
.
359
8.2
FOURIER
EXPANSION
OF
EISENSTEIN
SERIES
FOR
PSL(2,
O')
.
363
TABLE
OF
CONTENTS
XV
8.3
MEROMORPHIC
CONTINUATION
BY
FOURIER
EXPANSION
AND
THE
KRONECKER
LIMIT
FORMULA
.
370
8.4
SPECIAL
VALUES
OF
EISENSTEIN
SERIES
.
380
8.5
APPLICATIONS
TO
ZETA
FUNCTIONS
AND
ASYMPTOTICS
OF
DIVISOR
SUMS
.
393
8.6
NON-VANISHING
OF
L-FUNCTIONS
.
397
8.7
MEROMORPHIC
CONTINUATION
BY
INTEGRAL
REPRESENTATION
.
400
8.8
COMPUTATION
OF
THE
VOLUME
.
402
8.9
WEYL
'
S
ASYMPTOTIC
LAW
.
404
9.
INTEGRAL
BINARY
HERMITIAN
FORMS
.
407
9.1
UPPER
HALF-SPACE
AND
BINARY
HERMITIAN
FORMS
.
407
9.2
REDUCTION
THEORY
.
410
9.3
REPRESENTATION
NUMBERS
OF
BINARY
HERMITIAN
FORMS
.
414
9.4
ZETA
FUNCTIONS
FOR
BINARY
HERMITIAN
FORMS
.
425
9.5
THE
MASS-FORMULA
.
430
9.6
COMPUTATION
OF
THE
COVOLUME
OF
PSL(2,
O)
A
LA
HUMBERT
.
436
9.7
NOTES
AND
REMARKS
.
441
10.
EXAMPLES
OF
DISCONTINUOUS
GROUPS
.
443
10.1
GROUPS
OF
QUATERNIONS
.
444
10.2
UNIT
GROUPS
OF
QUADRATIC
FORMS
.
456
10.3
ARITHMETIC
AND
NON-ARITHMETIC
DISCRETE
GROUPS
.
477
10.4
THE
TETRAHEDRAL
GROUPS
.
480
10.5
NOTES
AND
REMARKS
.
494
REFERENCES
.
497
SUBJECT.
INDEX
.
521 |
| any_adam_object | 1 |
| author | Elstrodt, Jürgen 1940- Grunewald, Fritz 1949-2010 Mennicke, Jens 1931- |
| author_GND | (DE-588)11570597X (DE-588)115706011 (DE-588)115706062 |
| author_facet | Elstrodt, Jürgen 1940- Grunewald, Fritz 1949-2010 Mennicke, Jens 1931- |
| author_role | aut aut aut |
| author_sort | Elstrodt, Jürgen 1940- |
| author_variant | j e je f g fg j m jm |
| building | Verbundindex |
| bvnumber | BV011577807 |
| callnumber-first | Q - Science |
| callnumber-label | QA320 |
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| callnumber-search | QA320 QA320 .E47 1998 |
| callnumber-sort | QA 3320 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 240 SK 370 |
| classification_tum | MAT 430f MAT 100f MAT 578f |
| ctrlnum | (OCoLC)60186639 (DE-599)BVBBV011577807 |
| dewey-full | 512/.7 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.7 512.7 |
| dewey-search | 512/.7 512.7 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011577807 |
| illustrated | Illustrated |
| indexdate | 2024-08-20T00:44:53Z |
| institution | BVB |
| isbn | 3540627456 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007796659 |
| oclc_num | 60186639 |
| open_access_boolean | |
| owner | DE-739 DE-91G DE-BY-TUM DE-20 DE-384 DE-29T DE-824 DE-634 |
| owner_facet | DE-739 DE-91G DE-BY-TUM DE-20 DE-384 DE-29T DE-824 DE-634 |
| physical | XV, 524 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Elstrodt, Jürgen 1940- Verfasser (DE-588)11570597X aut Groups acting on hyperbolic space harmonic analysis and number theory J. Elstrodt ; F. Grunewald ; J. Mennicke Berlin [u.a.] Springer 1997 XV, 524 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 497 - 520 Spectral theory (Mathematics) Selberg trace formula Automorphic forms Functions, Zeta Automorphe Funktion (DE-588)4143706-8 gnd rswk-swf Gruppenoperation (DE-588)4158467-3 gnd rswk-swf Hyperbolischer Raum (DE-588)4161046-5 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Hyperbolischer Raum (DE-588)4161046-5 s Diskrete Gruppe (DE-588)4135541-6 s Gruppenoperation (DE-588)4158467-3 s Automorphe Funktion (DE-588)4143706-8 s DE-604 Grunewald, Fritz 1949-2010 Verfasser (DE-588)115706011 aut Mennicke, Jens 1931- Verfasser (DE-588)115706062 aut text/html http://www.loc.gov/catdir/enhancements/fy0812/97038717-d.html Publisher description text/html http://www.loc.gov/catdir/enhancements/fy0812/97038717-t.html Table of contents only DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007796659&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elstrodt, Jürgen 1940- Grunewald, Fritz 1949-2010 Mennicke, Jens 1931- Groups acting on hyperbolic space harmonic analysis and number theory Spectral theory (Mathematics) Selberg trace formula Automorphic forms Functions, Zeta Automorphe Funktion (DE-588)4143706-8 gnd Gruppenoperation (DE-588)4158467-3 gnd Hyperbolischer Raum (DE-588)4161046-5 gnd Diskrete Gruppe (DE-588)4135541-6 gnd |
| subject_GND | (DE-588)4143706-8 (DE-588)4158467-3 (DE-588)4161046-5 (DE-588)4135541-6 |
| title | Groups acting on hyperbolic space harmonic analysis and number theory |
| title_auth | Groups acting on hyperbolic space harmonic analysis and number theory |
| title_exact_search | Groups acting on hyperbolic space harmonic analysis and number theory |
| title_full | Groups acting on hyperbolic space harmonic analysis and number theory J. Elstrodt ; F. Grunewald ; J. Mennicke |
| title_fullStr | Groups acting on hyperbolic space harmonic analysis and number theory J. Elstrodt ; F. Grunewald ; J. Mennicke |
| title_full_unstemmed | Groups acting on hyperbolic space harmonic analysis and number theory J. Elstrodt ; F. Grunewald ; J. Mennicke |
| title_short | Groups acting on hyperbolic space |
| title_sort | groups acting on hyperbolic space harmonic analysis and number theory |
| title_sub | harmonic analysis and number theory |
| topic | Spectral theory (Mathematics) Selberg trace formula Automorphic forms Functions, Zeta Automorphe Funktion (DE-588)4143706-8 gnd Gruppenoperation (DE-588)4158467-3 gnd Hyperbolischer Raum (DE-588)4161046-5 gnd Diskrete Gruppe (DE-588)4135541-6 gnd |
| topic_facet | Spectral theory (Mathematics) Selberg trace formula Automorphic forms Functions, Zeta Automorphe Funktion Gruppenoperation Hyperbolischer Raum Diskrete Gruppe |
| url | http://www.loc.gov/catdir/enhancements/fy0812/97038717-d.html http://www.loc.gov/catdir/enhancements/fy0812/97038717-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007796659&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT elstrodtjurgen groupsactingonhyperbolicspaceharmonicanalysisandnumbertheory AT grunewaldfritz groupsactingonhyperbolicspaceharmonicanalysisandnumbertheory AT mennickejens groupsactingonhyperbolicspaceharmonicanalysisandnumbertheory |