Algebraic functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, NY
Dover Publications
2004
|
| Edition: | [Nachdr. d. Ausg. New York : AMS, 1933] |
| Series: | Dover phoenix editions
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 218 S. Ill., graph. Darst. |
| ISBN: | 048649568X |
Staff View
MARC
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| 245 | 1 | 0 | |a Algebraic functions |c Gilbert Ames Bliss |
| 250 | |a [Nachdr. d. Ausg. New York : AMS, 1933] | ||
| 264 | 1 | |a Mineola, NY |b Dover Publications |c 2004 | |
| 300 | |a IX, 218 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Dover phoenix editions | |
| 650 | 4 | |a Algebraic functions | |
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Record in the Search Index
| _version_ | 1804141128421736448 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
chapter i
Single-Valued Analytic Functions
Section Page
1.
Introduction
.............. 1
2.
Integrals of
f
unctions
ƒ
(z)
.......... 1
3.
Cauchy s theorem
.............. 2
4.
Consequences of Cauchy s theorem
........ 7
5.
Ordinary and singular points
......... 9
6.
Rational functions
............ 12
7.
An expansion theorem
........... 17
8.
Resultants and discriminants
......... 18
9.
Reducibility of a polynomial f(x, y)
....... 21
References for Chapter I
........... 23
chapter ii
Algebraic Functions and Their Expansions
10.
Introduction
.............. 24
11.
Definition of an algebraic function
........ 24
12.
Continuations of the values of an algebraic function
... 25
13.
The expansions for an algebraic function
...... 29
14.
Determination of the expansions by means of Newton s poly¬
gons
................ 35
15.
The polygon method gives all expansions
...... 37
16.
Special types of singular points
......... 40
References for Chapter II
.......... 42
chapter iii
Rational Functions
17.
Introduction
.............. 43
18.
First properties of rational functions
....... 43
19.
Bases for all rational functions
......... 46
20.
Divisors and their bases
........... 47
21.
Multiples of a divisor
........... 51
22.
Complementary bases
........... 59
23.
The invariant property of the genus number
..... 62
24.
Construction of elementary integrals
....... 64
25.
The Riemann-Roch theorem
......... 67
26.
Rational functions with prescribed poles
...... 70
References for Chapter III
.......... 74
CHAPTER IV
The Riemann Surface of an Algebraic Function
27.
Introduction
.............. 75
28.
The construction of the Riemann surface
Τ
..... 75
Section Page
29.
Holomorphic functions on a Riemann surface
..... 80
30.
Cauchy s theorem
............ . . 82
31.
Connectivity of a Riemann surface
....... 86
32.
Canonical systems of cuts making
Τ
simply connected
. . 90
References for Chapter IV
.......... 92
CHAPTER V
Integrals of Rational Functions
33.
Introduction
.............. 93
34.
Singularities and periods of integrals
....... 94
35.
Integrals of the first kind
.......... 98
36.
Expressions for an integral in terms of elementary integrals or
fundamental systems
........... 102
37.
Relations between periods of integrals
....... 105
38.
Construction of fundamental systems
....... 107
39.
Normal integrals
............. 110
40.
Expressions for rational functions in terms of integrals
. . 113
References for Chapter V
.......... 118
chapter vi
Abel s Theorem
41.
Introduction
............... 119
42.
A first form of Abel s theorem
......... 119
43.
Elementary applications of Abel s theorem
..... 121
44.
Addition formulas for elliptic integrals
....... 123
45.
Abel s theorem in more general form
....... 126
46.
An expression for
^+1
integrals in terms of
p
integrals
. . 129
47.
Proof of a lemma
............. 131
References for Chapter VI
.......... 132
chapter
vii
Birational
Transformations
48.
Introduction
.............. 133
49. Birational
transformations
.......... 134
50.
Curves of genus p = 0
οτ
p=l, and hyperelliptic curves
. . 139
51.
Projective
transformations
.......... 144
52.
A second formula for the genus
......... 147
53.
The number of
projective
intersections of two curves
. . 150
54.
A formula for integrand functions
ψ
of integrals of the first
kind
................ 151
References for Chapter
VII
.......... 154
CHAPTER
VIII
The Reduction of Singularities by Transformation
55.
Introduction
.............. 155
56.
Reduction of singularities to multiple points with distinct
tangents
.............. . 156
57.
Curves in the
projective
plane with double points only
. . 159
Section Page
58.
Reduction of singularities in the
projective
plane to double
points with distinct tangents
. ...... 163
59.
Curves in the function-theoretic plane with double points
only
................ 165
60.
Reduction of singularities in the function-theoretic plane to
double points with distinct tangents
....... 167
References for Chapter
VIII......... 168
chapter ix
Inversion of Abelian Integrals
61.
Introduction
.............. 169
62.
Integrals which define single-valued inverses
..... 170
63.
Inverse functions for the case p — Q
........ 171
64.
Inverse
f
unctions when
ρ
— 1......... 172
65.
Analogies between elliptic functions and rational functions of
χ
and
y
............... 174
66.
Further remarks concerning elliptic functions
..... 177
References for Chapter IX
.......... 182
chapter x
Examples
67.
Introduction
.............. 183
68.
Examples for expansions
........... 183
69.
Examples for Riemann surfaces
......... 186
70.
Elliptic and hyperelliptic curves
........ 189
71.
Normal forms for equations of the third degree in
y
. . . 194
72.
A basis
f
or the divisor Q—
1.......... 196
73.
The complementary basis
.......... 200
74.
A Theorem of Baur
............ 204
75.
Applications to equations of the third degree in
y
. . . 207
76.
Equations of the fourth degree in
χ
and
y
...... 210
77.
Examples
.............. . 211
References for Chapter X
.......... 213
List of References
214
|
| any_adam_object | 1 |
| author | Bliss, Gilbert Ames 1876-1951 |
| author_GND | (DE-588)116202084 |
| author_facet | Bliss, Gilbert Ames 1876-1951 |
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| classification_rvk | SK 750 |
| ctrlnum | (OCoLC)54371889 (DE-599)BVBBV036074859 |
| dewey-full | 512.7/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | [Nachdr. d. Ausg. New York : AMS, 1933] |
| format | Book |
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| id | DE-604.BV036074859 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:10:57Z |
| institution | BVB |
| isbn | 048649568X |
| language | English |
| lccn | 2004043837 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018966052 |
| oclc_num | 54371889 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | IX, 218 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Dover Publications |
| record_format | marc |
| series2 | Dover phoenix editions |
| spelling | Bliss, Gilbert Ames 1876-1951 Verfasser (DE-588)116202084 aut Algebraic functions Gilbert Ames Bliss [Nachdr. d. Ausg. New York : AMS, 1933] Mineola, NY Dover Publications 2004 IX, 218 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dover phoenix editions Algebraic functions Algebraische Funktion (DE-588)4141836-0 gnd rswk-swf Algebraische Funktion (DE-588)4141836-0 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018966052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bliss, Gilbert Ames 1876-1951 Algebraic functions Algebraic functions Algebraische Funktion (DE-588)4141836-0 gnd |
| subject_GND | (DE-588)4141836-0 |
| title | Algebraic functions |
| title_auth | Algebraic functions |
| title_exact_search | Algebraic functions |
| title_full | Algebraic functions Gilbert Ames Bliss |
| title_fullStr | Algebraic functions Gilbert Ames Bliss |
| title_full_unstemmed | Algebraic functions Gilbert Ames Bliss |
| title_short | Algebraic functions |
| title_sort | algebraic functions |
| topic | Algebraic functions Algebraische Funktion (DE-588)4141836-0 gnd |
| topic_facet | Algebraic functions Algebraische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018966052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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