Spectral theory of automorphic functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence ; Rhode Island
American Mathematical Society
1982
|
| Series: | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics
153 = 1982,4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russischen übersetzt |
| Physical Description: | ix, 163 Seiten |
| ISBN: | 0821830783 |
Staff View
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| 245 | 1 | 0 | |a Spectral theory of automorphic functions |c by A. B. Venkov |
| 264 | 1 | |a Providence ; Rhode Island |b American Mathematical Society |c 1982 | |
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Record in the Search Index
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| adam_text | PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
IN THE ACADEMY OF SCIENCES OF THE USSR
TABLE OF CONTENTS
Introduction 1
CHAPTER 1. Notation and auxiliary theorems 11
§1.1. The Laplace operator for the Poincare metric on the Lobachevsky
plane 11
§1.2. Fuchsian group of the first kind F, its fundamental domain F, and
the representation X Series over the group F 12
§1.3. Function spaces and integral operators 14
§1.4. The operator 2l(F;x) and its resolvent 9J(s;F;x) 16
CHAPTER 2. Theorem on expansion in eigenfunctions of the operator
2l(F;X) 19
§2.1. Properties of the resolvent 9}(s;F;x) far from the spectrum 19
§2.2. Faddeev s integral equation and analytic continuation of the
resolvent 5R(s;F;x) to the half plane Res 0 27
§2.3. Eigenfunctions of the continuous spectrum of 2l(F; x) and spectral
decomposition 35
CHAPTER 3. First refinement of the expansion theorem for SI(F; x). The
continuous spectrum 43
§3.1. Eisenstein series 43
§3.2. The Maass Selberg relation 48
§3.3. Incomplete theta series and cusp vector functions. The operators
K(r,x) so
§3.4. The Selberg Neunhoffer integral equation 55
§3.5. The determinant of the scattering matrix 59
CHAPTER 4. The Selberg trace formula 63
§4.1. Nuclearity of the operator K(T;x)%(X;x) 63
§4.2. Justification of the spectral trace formula 65
§4.3. Derivation of the Selberg trace formula 67
§4.4. The Weyl Selberg asymptotic formula. Extension of the Selberg
trace formula to a broader class of functions h 77
CHAPTER 5. Elements of the theory of the Selberg zeta function. Spectral
and geometric applications of the theory 81
§5.1. The definitions and basic properties of Z(s; F; x) 81
§5.2. Remainder estimate for the Weyl Selberg formula 86
§5.3. Asymptotic formula for the distribution function tt(x;F) 93
CHAPTER 6. Second refinement of the expansion theorem for 3l(P;x). The
discrete spectrum 97
§6.1. Problems in the theory of the discrete spectrum. The spectrum of
2l(P; 1) for congruence subgroups P 97
§6.2. Elements of Artin theory in the spectral theory of automorphic
functions, and Roelcke s conjecture 102
§6.3. The spectrum of 2l(r;l) for a group T £ W with nontrivial
commensurable 108
§6.4. The spectrum of 2l(P; 1) for a group P commensurable with the
group TM 118
§6.5. Selberg trace formula for the Dirichlet boundary value problem on
a regular polygon M 124
§6.6. Elements of the theory of the Selberg zeta function for the
Dirichlet boundary value problem on a regular polygon 138
§6.7. Estimate of the remainder in Weyl s formula for the Dirichlet
boundary value problem on M 143
CHAPTER 7. The spectral theory of perturbations of the spectrum of the
operator 3l(P;x) Some perspectives on the development of the spectral
theory of automorphic functions 149
§7.1. Deformations of the group P, the spectrum of 2I(P; x), and singular
points of the resolvent $(s;P;x) 149
§7.2. Zeros of zeta and L functions of imaginary quadratic fields and
the eigenvalues of SI(PZ; 1) 153
Bibliography 161
|
| any_adam_object | 1 |
| author | Venkov, Aleksej B. |
| author_GND | (DE-588)1061193764 |
| author_facet | Venkov, Aleksej B. |
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| author_sort | Venkov, Aleksej B. |
| author_variant | a b v ab abv |
| building | Verbundindex |
| bvnumber | BV000246210 |
| classification_rvk | SI 700 |
| ctrlnum | (OCoLC)260150993 (DE-599)BVBBV000246210 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000246210 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:11:02Z |
| institution | BVB |
| isbn | 0821830783 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000148150 |
| oclc_num | 260150993 |
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| owner_facet | DE-12 DE-384 DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-11 DE-188 DE-83 |
| physical | ix, 163 Seiten |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| series2 | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| spelling | Venkov, Aleksej B. (DE-588)1061193764 aut Spektral'naja teorija avtomorfnych funkcij Spectral theory of automorphic functions by A. B. Venkov Providence ; Rhode Island American Mathematical Society 1982 ix, 163 Seiten txt rdacontent n rdamedia nc rdacarrier Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 153 = 1982,4 Aus dem Russischen übersetzt Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Funktion (DE-588)4143706-8 gnd rswk-swf Automorphe Funktion (DE-588)4143706-8 s Spektraltheorie (DE-588)4116561-5 s DE-604 Automorphe Form (DE-588)4003972-9 s Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 153 = 1982,4 (DE-604)BV000009943 153 = 1982,4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000148150&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Venkov, Aleksej B. Spectral theory of automorphic functions Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics Spektraltheorie (DE-588)4116561-5 gnd Automorphe Form (DE-588)4003972-9 gnd Automorphe Funktion (DE-588)4143706-8 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4003972-9 (DE-588)4143706-8 |
| title | Spectral theory of automorphic functions |
| title_alt | Spektral'naja teorija avtomorfnych funkcij |
| title_auth | Spectral theory of automorphic functions |
| title_exact_search | Spectral theory of automorphic functions |
| title_full | Spectral theory of automorphic functions by A. B. Venkov |
| title_fullStr | Spectral theory of automorphic functions by A. B. Venkov |
| title_full_unstemmed | Spectral theory of automorphic functions by A. B. Venkov |
| title_short | Spectral theory of automorphic functions |
| title_sort | spectral theory of automorphic functions |
| topic | Spektraltheorie (DE-588)4116561-5 gnd Automorphe Form (DE-588)4003972-9 gnd Automorphe Funktion (DE-588)4143706-8 gnd |
| topic_facet | Spektraltheorie Automorphe Form Automorphe Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000148150&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000009943 |
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