Lectures on Dirichlet series, modular functions and quadratic forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Göttingen
Vandenhoeck & Ruprecht
1983
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 98 Seiten graph. Darst. |
| ISBN: | 3525407270 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lectures on Dirichlet series, modular functions and quadratic forms |c Erich Hecke |
| 264 | 1 | |a Göttingen |b Vandenhoeck & Ruprecht |c 1983 | |
| 300 | |a 98 Seiten |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804120744280457216 |
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| adam_text | Table of Contents
Introduction
1. The Riemann zeta-function 7
2. Associated Dirichlet series and power series 12
3. The Euler product 15
4. Quadratic forms 18
Chapter I. The first main theorem
1. The correspondence between Dirichlet series and power series 21
2. The group ©(A). The transformation of the power series 24
Chapter II. The case A 2
1. Definition and determination of fundamental region 27
2. The local uniformising variable 30
3. Existence of automorphic forms 31
Chapter III. The case A 2
1. The finiteness of the number of solutions 34
2. The possible values of A and k 37
3. The number of solutions 40
4. The existence of solutions 42
5. The O-assertion 46
6. The modular case 48
7. Construction of solutions for A / 1 from those for A = 1 50
Chapter IV. The case A = 2
1. The region F 54
2. The order of the forms 56
3. The number of functions /(t) 58
4. Special cases 62
5. Concluding remarks 66
Chapter V. The Euler product
1. Entire forms 68
2. The substitution L of order n 68
3. The operator T(ri) 70
4. The second main theorem 76
5. The Euler product 77
6. Eigen-function of the operator-ring 78
5
7. Cusp-forms 81
8. Concluding remarks 82
Chapter VI. The connection with quadratic forms
1. The multiple theta-series 84
2. Some special cases 86
Chapter VII. Generalisation to systems of Dirichlet series
1. The zeta-function for imaginary quadratic fields K( / — D) 90
2. The general formulation 93
3. The case X = q 95
|
| any_adam_object | 1 |
| author | Hecke, Erich 1887-1947 |
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| dewey-full | 515.9 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV006484527 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:46:57Z |
| institution | BVB |
| isbn | 3525407270 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004121106 |
| oclc_num | 9814017 |
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| physical | 98 Seiten graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Vandenhoeck & Ruprecht |
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| spelling | Hecke, Erich 1887-1947 Verfasser (DE-588)119045133 aut Lectures on Dirichlet series, modular functions and quadratic forms Erich Hecke Göttingen Vandenhoeck & Ruprecht 1983 98 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dirichlet series Forms, Quadratic Modular functions Dirichlet-Reihe (DE-588)4150139-1 gnd rswk-swf Quadratische Form (DE-588)4128297-8 gnd rswk-swf Dirichlet-Reihe (DE-588)4150139-1 s Quadratische Form (DE-588)4128297-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004121106&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hecke, Erich 1887-1947 Lectures on Dirichlet series, modular functions and quadratic forms Dirichlet series Forms, Quadratic Modular functions Dirichlet-Reihe (DE-588)4150139-1 gnd Quadratische Form (DE-588)4128297-8 gnd |
| subject_GND | (DE-588)4150139-1 (DE-588)4128297-8 |
| title | Lectures on Dirichlet series, modular functions and quadratic forms |
| title_auth | Lectures on Dirichlet series, modular functions and quadratic forms |
| title_exact_search | Lectures on Dirichlet series, modular functions and quadratic forms |
| title_full | Lectures on Dirichlet series, modular functions and quadratic forms Erich Hecke |
| title_fullStr | Lectures on Dirichlet series, modular functions and quadratic forms Erich Hecke |
| title_full_unstemmed | Lectures on Dirichlet series, modular functions and quadratic forms Erich Hecke |
| title_short | Lectures on Dirichlet series, modular functions and quadratic forms |
| title_sort | lectures on dirichlet series modular functions and quadratic forms |
| topic | Dirichlet series Forms, Quadratic Modular functions Dirichlet-Reihe (DE-588)4150139-1 gnd Quadratische Form (DE-588)4128297-8 gnd |
| topic_facet | Dirichlet series Forms, Quadratic Modular functions Dirichlet-Reihe Quadratische Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004121106&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT heckeerich lecturesondirichletseriesmodularfunctionsandquadraticforms |