Theta functions with applications to Riemann surfaces:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Baltimore
Williams & Wilkins
1974
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 232 S. graph. Darst. |
| ISBN: | 0683071963 |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS
PART 1. GENERAL THETA FUNCTIONS 1
Chapter I.
Definitions and basic properties of theta functions with characteristics... 3
Chapter II.
Theta indices and theta identities 19
1. Introduction and sample identities 19
2. The formal development of the calculus of theta indices 25
3. The theta identities 42
Appendix 1 to Chapter II.
Explicit construction of principal sets of characteristics 55
Appendix 2 to Chapter II.
Some identities obtained by rearrangement of summation 60
Appendix 3 to Chapter II.
The Riemann theta formula 66
Chapter HI.
Transformation Theory 73
0. Introductory Remark 73
1. Motivation from Riemann surface theory 73
2. Some essential definitions and lemmas 82
3. Linear transformation of the thetas—Main theorems 86
4. Proof of Theorem A 90
5. Proof of Theorem B and Lemmas A and B 97
6. Proof of Theorem C 99
7. Proof of Theorem D 100
8. A numerical example 105
PART 2. APPLICATIONS TO RIEMANN SURFACES 117
Chapter IV.
Riemann surface theory 119
1. Introduction 119
2. Definition of a Riemann surface 119
3. Topology of Riemann surfaces 122
xi
xii CONTENTS
4. Differentials on a Riemann surface 127
5. Existence theorems 130
6. Periods of holomorphic and meromorphic differentials 130
7. The Riemann Roch theorem and Abel s theorem 135
8. Hyperelliptic surfaces 144
Appendix to Chapter IV.
An example: the surface w2 = z6 — z and the matrix v 155
Chapter V.
Theta functions on a Riemann surface 160
1. Basic theorems 160
2. Some applications of the basic theorems 175
3. Some special results on hyperelliptic surfaces 181
Chapter VI.
Applications of the theory of theta functions to Riemann surfaces 187
1. Introduction 187
2. Period relations 188
3. Relations among quadratic differentials 218
Appendix 1 to Chapter VI.
Moduli and theta functions 221
Appendix 2 to Chapter VI.
Functional independence of Schottky type period relations for
genus five 222
Index 231
|
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| id | DE-604.BV007389427 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:01:15Z |
| institution | BVB |
| isbn | 0683071963 |
| language | English |
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| physical | XII, 232 S. graph. Darst. |
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| publishDate | 1974 |
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| publisher | Williams & Wilkins |
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| spelling | Rauch, Harry E. Verfasser aut Theta functions with applications to Riemann surfaces Harry E. Rauch ; Hershel M. Farkas Baltimore Williams & Wilkins 1974 XII, 232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fonctions thêta Riemann, Surfaces de Functions, Theta Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Thetafunktion (DE-588)4185175-4 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s DE-604 Thetafunktion (DE-588)4185175-4 s Farkas, Hershel M. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004776075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rauch, Harry E. Farkas, Hershel M. Theta functions with applications to Riemann surfaces Fonctions thêta Riemann, Surfaces de Functions, Theta Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd Thetafunktion (DE-588)4185175-4 gnd |
| subject_GND | (DE-588)4049991-1 (DE-588)4185175-4 |
| title | Theta functions with applications to Riemann surfaces |
| title_auth | Theta functions with applications to Riemann surfaces |
| title_exact_search | Theta functions with applications to Riemann surfaces |
| title_full | Theta functions with applications to Riemann surfaces Harry E. Rauch ; Hershel M. Farkas |
| title_fullStr | Theta functions with applications to Riemann surfaces Harry E. Rauch ; Hershel M. Farkas |
| title_full_unstemmed | Theta functions with applications to Riemann surfaces Harry E. Rauch ; Hershel M. Farkas |
| title_short | Theta functions with applications to Riemann surfaces |
| title_sort | theta functions with applications to riemann surfaces |
| topic | Fonctions thêta Riemann, Surfaces de Functions, Theta Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd Thetafunktion (DE-588)4185175-4 gnd |
| topic_facet | Fonctions thêta Riemann, Surfaces de Functions, Theta Riemann surfaces Riemannsche Fläche Thetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004776075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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