An approach to the Selberg trace formula via the Selberg zeta-function:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
Springer
[1987]
|
| Series: | Lecture notes in mathematics
1253 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 184 Seiten |
| ISBN: | 3540152083 0387152083 |
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| 100 | 1 | |a Fischer, Jürgen |d 1946- |0 (DE-588)14338001X |4 aut | |
| 245 | 1 | 0 | |a An approach to the Selberg trace formula via the Selberg zeta-function |c Jürgen Fischer |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c [1987] | |
| 264 | 4 | |c © 1987 | |
| 300 | |a 184 Seiten | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1253 | |
| 650 | 4 | |a Fonctions zêta | |
| 650 | 4 | |a Selberg, Formule de trace de | |
| 650 | 4 | |a Functions, Zeta | |
| 650 | 4 | |a Selberg trace formula | |
| 650 | 0 | 7 | |a Selberg-Spurformel |0 (DE-588)4248208-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Selberg-Zetafunktion |0 (DE-588)4314111-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1809991530435313664 |
|---|---|
| adam_text |
TABLE OF CONTENTS
page
Introduction
The mathematical background 1
The contents of this volume 7
1. Basic facts 14
1.1 Notations 14
1.2 Cofinite groups, fundamental domains 15
1.3 The linear operators .|[3,k], multiplier systems 17
1.4 The eigenvalue problem of automorphic forms, ^
the resolvent of the differential operator A. 22
1.5 Eisenstein series 28
1.6 Spectral decomposition of A, , orthogonal series
expansion in 1)^ 35
2. The trace of the iterated resolvent kernel 40
2.1 Representation of the trace by the eigenvalues of A, 41
2.2 The contribution of the hyperbolic elements 47
2.3 The contribution of the elliptic elements 57
2.4 The contribution of the parabolic elements 69
2.5 The resolvent trace formula 105
3. The entire function 5 associated with the
Selberg zeta function 113
3.1 Definition and functional equation of E ,
the Selberg zeta function 113
3.2 The grov/th of H 117
3.3 The distribution of the eigenvalues of Ak ,
the Weyl Selberg asymptotic formula 127
3.4 WeierstraB factorization of the entire function H ,
an analogue of the Euler Mascheroni constant 145
4. The general Selberg trace formula 162
Index 176
Index of notations 177
References 180 |
| any_adam_object | 1 |
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| dewey-full | 512/.7 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.7 510 |
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| genre | Selbergsche Zetafunktion gnd |
| genre_facet | Selbergsche Zetafunktion |
| id | DE-604.BV000681258 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-12T12:00:35Z |
| institution | BVB |
| isbn | 3540152083 0387152083 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000425042 |
| oclc_num | 230848262 |
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| physical | 184 Seiten |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Fischer, Jürgen 1946- (DE-588)14338001X aut An approach to the Selberg trace formula via the Selberg zeta-function Jürgen Fischer Berlin, [u.a.] Springer [1987] © 1987 184 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1253 Fonctions zêta Selberg, Formule de trace de Functions, Zeta Selberg trace formula Selberg-Spurformel (DE-588)4248208-2 gnd rswk-swf Selberg-Zetafunktion (DE-588)4314111-0 gnd rswk-swf Selberg-Spurformel (DE-588)4248208-2 s Selberg-Zetafunktion (DE-588)4314111-0 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-39331-3 Lecture notes in mathematics 1253 (DE-604)BV000676446 1253 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000425042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fischer, Jürgen 1946- An approach to the Selberg trace formula via the Selberg zeta-function Lecture notes in mathematics Fonctions zêta Selberg, Formule de trace de Functions, Zeta Selberg trace formula Selberg-Spurformel (DE-588)4248208-2 gnd Selberg-Zetafunktion (DE-588)4314111-0 gnd |
| subject_GND | (DE-588)4248208-2 (DE-588)4314111-0 |
| title | An approach to the Selberg trace formula via the Selberg zeta-function |
| title_auth | An approach to the Selberg trace formula via the Selberg zeta-function |
| title_exact_search | An approach to the Selberg trace formula via the Selberg zeta-function |
| title_full | An approach to the Selberg trace formula via the Selberg zeta-function Jürgen Fischer |
| title_fullStr | An approach to the Selberg trace formula via the Selberg zeta-function Jürgen Fischer |
| title_full_unstemmed | An approach to the Selberg trace formula via the Selberg zeta-function Jürgen Fischer |
| title_short | An approach to the Selberg trace formula via the Selberg zeta-function |
| title_sort | an approach to the selberg trace formula via the selberg zeta function |
| topic | Fonctions zêta Selberg, Formule de trace de Functions, Zeta Selberg trace formula Selberg-Spurformel (DE-588)4248208-2 gnd Selberg-Zetafunktion (DE-588)4314111-0 gnd |
| topic_facet | Fonctions zêta Selberg, Formule de trace de Functions, Zeta Selberg trace formula Selberg-Spurformel Selberg-Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000425042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT fischerjurgen anapproachtotheselbergtraceformulaviatheselbergzetafunction |