The spectrum of hyperbolic surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham
Springer
[2016]
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Abstract Inhaltsverzeichnis |
| Physical Description: | 1 Online Ressource (XIII, 370 Seiten, 8 illus. in color) |
| ISBN: | 9783319276663 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-319-27666-3 |
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Record in the Search Index
| _version_ | 1804176018147115008 |
|---|---|
| adam_text | THE SPECTRUM OF HYPERBOLIC SURFACES
/ BERGERON, NICOLAS
: 2016
ABSTRACT / INHALTSTEXT
THIS TEXT IS AN INTRODUCTION TO THE SPECTRAL THEORY OF THE LAPLACIAN ON
COMPACT OR FINITE AREA HYPERBOLIC SURFACES. FOR SOME OF THESE SURFACES,
CALLED “ARITHMETIC HYPERBOLIC SURFACES”, THE EIGENFUNCTIONS ARE OF
ARITHMETIC NATURE, AND ONE MAY USE ANALYTIC TOOLS AS WELL AS POWERFUL
METHODS IN NUMBER THEORY TO STUDY THEM. AFTER AN INTRODUCTION TO THE
HYPERBOLIC GEOMETRY OF SURFACES, WITH A SPECIAL EMPHASIS ON THOSE OF
ARITHMETIC TYPE, AND THEN AN INTRODUCTION TO SPECTRAL ANALYTIC METHODS
ON THE LAPLACE OPERATOR ON THESE SURFACES, THE AUTHOR DEVELOPS THE
ANALOGY BETWEEN GEOMETRY (CLOSED GEODESICS) AND ARITHMETIC (PRIME
NUMBERS) IN PROVING THE SELBERG TRACE FORMULA. ALONG WITH IMPORTANT
NUMBER THEORETIC APPLICATIONS, THE AUTHOR EXHIBITS APPLICATIONS OF THESE
TOOLS TO THE SPECTRAL STATISTICS OF THE LAPLACIAN AND THE QUANTUM UNIQUE
ERGODICITY PROPERTY. THE LATTER REFERS TO THE ARITHMETIC QUANTUM UNIQUE
ERGODICITY THEOREM, RECENTLY PROVED BY ELON LINDENSTRAUSS. THE FRUIT OF
SEVERAL GRADUATE LEVEL COURSES AT ORSAY AND JUSSIEU, THE SPECTRUM OF
HYPERBOLIC SURFACES ALLOWS THE READER TO REVIEW AN ARRAY OF CLASSICAL
RESULTS AND THEN TO BE LED TOWARDS VERY ACTIVE AREAS IN MODERN
MATHEMATICS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
THE SPECTRUM OF HYPERBOLIC SURFACES
/ BERGERON, NICOLAS
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
INTRODUCTION
ARITHMETIC HYPERBOLIC SURFACES
SPECTRAL DECOMPOSITION
MAASS FORMS
THE TRACE FORMULA
MULTIPLICITY OF LAMBDA1 AND THE SELBERG CONJECTURE
L-FUNCTIONS AND THE SELBERG CONJECTURE
JACQUET-LANGLANDS CORRESPONDENCE
ARITHMETIC QUANTUM UNIQUE ERGODICITY
APPENDICES
REFERENCES
INDEX OF NOTATION
INDEX
INDEX OF NAMES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Bergeron, Nicolas 1975-2024 |
| author_GND | (DE-588)133056996 |
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| author_role | aut |
| author_sort | Bergeron, Nicolas 1975-2024 |
| author_variant | n b nb |
| building | Verbundindex |
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| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-27666-3 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:25:30Z |
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| isbn | 9783319276663 |
| issn | 0172-5939 |
| language | English |
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| spelling | Bergeron, Nicolas 1975-2024 Verfasser (DE-588)133056996 aut The spectrum of hyperbolic surfaces Nicolas Bergeron Cham Springer [2016] © 2016 1 Online Ressource (XIII, 370 Seiten, 8 illus. in color) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Mathematics Harmonic analysis Dynamics Ergodic theory Hyperbolic geometry Hyperbolic Geometry Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Mathematik Erscheint auch als Druckausgabe 978-3-319-27664-9 https://doi.org/10.1007/978-3-319-27666-3 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840952&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840952&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bergeron, Nicolas 1975-2024 The spectrum of hyperbolic surfaces Mathematics Harmonic analysis Dynamics Ergodic theory Hyperbolic geometry Hyperbolic Geometry Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Mathematik |
| title | The spectrum of hyperbolic surfaces |
| title_auth | The spectrum of hyperbolic surfaces |
| title_exact_search | The spectrum of hyperbolic surfaces |
| title_full | The spectrum of hyperbolic surfaces Nicolas Bergeron |
| title_fullStr | The spectrum of hyperbolic surfaces Nicolas Bergeron |
| title_full_unstemmed | The spectrum of hyperbolic surfaces Nicolas Bergeron |
| title_short | The spectrum of hyperbolic surfaces |
| title_sort | the spectrum of hyperbolic surfaces |
| topic | Mathematics Harmonic analysis Dynamics Ergodic theory Hyperbolic geometry Hyperbolic Geometry Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Mathematik |
| topic_facet | Mathematics Harmonic analysis Dynamics Ergodic theory Hyperbolic geometry Hyperbolic Geometry Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Mathematik |
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