Theory of algebraic functions of one variable:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Providence, RI
American Mathematical Society
2012
|
| Series: | History of mathematics
39 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 152 S. graph. Darst. 26 cm |
| ISBN: | 9780821883303 |
Staff View
MARC
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| 100 | 1 | |a Dedekind, Richard |d 1831-1916 |e Verfasser |0 (DE-588)118524259 |4 aut | |
| 240 | 1 | 0 | |a Theorie der algebraischen Functionen einer Veränderlichen |
| 245 | 1 | 0 | |a Theory of algebraic functions of one variable |c Richard Dedekind and Heinrich Weber ; Translated and Introduced by John Stillwell |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2012 | |
| 300 | |a VIII, 152 S. |b graph. Darst. |c 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a History of mathematics |v 39 | |
| 648 | 4 | |a Geschichte 1800-1900 | |
| 648 | 7 | |a Geschichte 1882 |2 gnd |9 rswk-swf | |
| 650 | 4 | |a Algebraic functions | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 7 | |a History and biography -- History of mathematics and mathematicians -- 19th century |2 msc | |
| 650 | 0 | 7 | |a Algebraische Funktion |0 (DE-588)4141836-0 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804149433416286208 |
|---|---|
| adam_text | Contents
Preface
vii
Translator s Introduction
1
1.
Overview
1
2.
Prom Calculus to Abel s Theory of Algebraic Curves
2
3.
Riemann s Theory of Algebraic Curves
6
4.
The Riemann-Hurwitz Formula
10
5.
Functions on Riemann Surfaces
12
6.
Later Development of Analysis on Riemann Surfaces
16
7.
Origins of Algebraic Number Theory
21
8.
Dedekind s Theory of Algebraic Integers
24
9.
Number Fields and Function Fields
27
10.
Algebraic Functions and Riemann Surfaces
31
11.
From Points to Valuations
34
12.
Reading the Dedekind-Weber Paper
35
13.
Conclusion
37
Theory of Algebraic Functions of One Variable
39
Introduction
41
Part I
45
§1.
Fields of algebraic functions
45
§2.
Norm, trace, and discriminant
47
§3.
The system of integral algebraic functions of
z
in the field
Ω
51
§4.
Modules of functions
55
§5.
Congruences
58
§6.
The norm of one module relative to another
60
§7.
The ideals in
о
65
§8.
Multiplication and division of ideals
67
§9.
Laws of divisibility of ideals
70
§10.
Complementary bases of the field
Ω
75
§11.
The ramification ideal
81
§12.
The fractional functions of
ζ
in the field
Ω
86
§13.
Rational transformations of functions in the field
Ω
89
Part II
93
§14.
The points of the Riemann surface
93
§15.
The order numbers
96
§16.
Conjugate points and conjugate values
99
§17.
Representing the functions in the field
Ω
by polygon quotients
103
vi
CONTENTS
§18.
Equivalent
polygons and polygon classes
104
§19.
Vector spaces of polygons
106
§20.
Lowering the dimension of the space by divisibility conditions
107
§21.
The dimensions of polygon classes
109
§22.
The normal bases of
о
110
§23.
The differential quotient
113
§24.
The genus of the field
Ω
118
§25.
The differentials in
Ω
121
§26.
Differentials of the first kind
123
§27.
Polygon classes of the first and second kind
126
§28.
The Riemann-Roch theorem for proper classes
127
§29.
The Riemann-Roch theorem for improper classes of the first kind
130
§30.
Improper classes of the second kind
131
§31.
Differentials of the second and third kinds
133
§32.
Residues
135
§33.
Relations between differentials of the first and second kinds
138
Bibliography
141
Index
145
|
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| dewey-full | 512.7/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/3 |
| dewey-search | 512.7/3 |
| dewey-sort | 3512.7 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte 1800-1900 Geschichte 1882 gnd |
| era_facet | Geschichte 1800-1900 Geschichte 1882 |
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| id | DE-604.BV040388361 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:22:57Z |
| institution | BVB |
| isbn | 9780821883303 |
| language | English German |
| lccn | 2012011949 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025241748 |
| oclc_num | 844021787 |
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| physical | VIII, 152 S. graph. Darst. 26 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | History of mathematics |
| series2 | History of mathematics |
| spelling | Dedekind, Richard 1831-1916 Verfasser (DE-588)118524259 aut Theorie der algebraischen Functionen einer Veränderlichen Theory of algebraic functions of one variable Richard Dedekind and Heinrich Weber ; Translated and Introduced by John Stillwell Providence, RI American Mathematical Society 2012 VIII, 152 S. graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier History of mathematics 39 Geschichte 1800-1900 Geschichte 1882 gnd rswk-swf Algebraic functions Geometry, Algebraic History and biography -- History of mathematics and mathematicians -- 19th century msc Algebraische Funktion (DE-588)4141836-0 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf (DE-588)4135952-5 Quelle gnd-content Algebraische Funktion (DE-588)4141836-0 s Algebraische Geometrie (DE-588)4001161-6 s Geschichte 1882 z DE-604 Weber, Heinrich 1842-1913 Verfasser (DE-588)1012808513 aut Erscheint auch als Online-Ausgabe 978-0-8218-9033-2 History of mathematics 39 (DE-604)BV001327576 39 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025241748&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dedekind, Richard 1831-1916 Weber, Heinrich 1842-1913 Theory of algebraic functions of one variable History of mathematics Algebraic functions Geometry, Algebraic History and biography -- History of mathematics and mathematicians -- 19th century msc Algebraische Funktion (DE-588)4141836-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4141836-0 (DE-588)4001161-6 (DE-588)4135952-5 |
| title | Theory of algebraic functions of one variable |
| title_alt | Theorie der algebraischen Functionen einer Veränderlichen |
| title_auth | Theory of algebraic functions of one variable |
| title_exact_search | Theory of algebraic functions of one variable |
| title_full | Theory of algebraic functions of one variable Richard Dedekind and Heinrich Weber ; Translated and Introduced by John Stillwell |
| title_fullStr | Theory of algebraic functions of one variable Richard Dedekind and Heinrich Weber ; Translated and Introduced by John Stillwell |
| title_full_unstemmed | Theory of algebraic functions of one variable Richard Dedekind and Heinrich Weber ; Translated and Introduced by John Stillwell |
| title_short | Theory of algebraic functions of one variable |
| title_sort | theory of algebraic functions of one variable |
| topic | Algebraic functions Geometry, Algebraic History and biography -- History of mathematics and mathematicians -- 19th century msc Algebraische Funktion (DE-588)4141836-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraic functions Geometry, Algebraic History and biography -- History of mathematics and mathematicians -- 19th century Algebraische Funktion Algebraische Geometrie Quelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025241748&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001327576 |
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