Elliptic functions and elliptic integrals:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1997
|
| Series: | Translations of mathematical monographs
170 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 185 S. graph. Darst. |
| ISBN: | 0821805878 |
Staff View
MARC
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| 100 | 1 | |a Prasolov, Viktor V. |d 1956- |e Verfasser |0 (DE-588)129271977 |4 aut | |
| 240 | 1 | 0 | |a Elliptičeskie funkcii i elliptičeskie integraly |
| 245 | 1 | 0 | |a Elliptic functions and elliptic integrals |c Viktor Prasolov ; Yuri Solovyev |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1997 | |
| 300 | |a X, 185 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 170 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Fonctions elliptiques |2 ram | |
| 650 | 4 | |a Elliptic functions | |
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| 650 | 0 | 7 | |a Elliptische Funktion |0 (DE-588)4134665-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Solov'ev, Jurij P. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804126539150786560 |
|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Geometry of Cubic Curves 1
§1.1. Addition of points on a cubic 1
§1.2. Lines and curves on the projective plane 8
§1.3. The tangents and inflection points 11
§1.4. Normal forms of the nonsingular cubic 16
§1.5. Singular cubics 20
§1.6. No nonsingular cubic admits a rational parameterization 22
Chapter 2. Elliptic Functions 25
§2.1. The topological structure of nonsingular cubics in CP2 26
§2.2. The elliptic functions 29
§2.3. The Weierstrass function 32
§2.4. A differential equation for the Weierstrass function p(z) 35
§2.5. A parameterization of the cubic with the help of the Weierstrass
function 36
§2.6. The elliptic integrals 39
§2.7. Addition theorems for the elliptic integrals F(tp) and E(ip) 44
§2.8. The elliptic Jacobi functions 46
§2.9. The Weierstrass theorem on functions possessing an algebraic ad¬
dition theorem 49
Chapter 3. Arcs of Curves and Elliptic Integrals 53
§3.1. Arcs of the ellipse and the hyperbola 53
§3.2. Division of arcs of the ellipse 55
§3.3. Curves with elliptic arcs 60
§3.4. Curves whose arc lengths can be expressed in terms of arc lengths
of the circle 64
Chapter 4. Abel s Theorem on Division of Lemniscate 67
§4.1. Construction of a regular 17 gon. An elementary approach 69
§4.2. Construction of regular polygons. Elements of Galois theory 71
§4.3. The equation for the division of the lemniscate 78
§4.4. Proof of Abel s theorem on the division of the lemniscate 86
§4.5. Several remarks on Serret s curves 91
Chapter 5. Arithmetic of Cubic Curves 103
§5.1. Diophantus method of secants. Second degree diophantine equa¬
tions 104
vii
viii CONTENTS
§5.2. Addition of points on a cubic curve 111
§5.3. Several examples 115
§5.4. Mordell s theorem 119
§5.5. The rank and the torsion group of an elliptic curve 124
Chapter 6. Algebraic Equations 131
§6.1. Solving cubic and quartic equations 131
§6.2. Symmetric polynomials 133
§6.3. The Lagrange resolvents 134
§6.4. Roots of unity 137
§6.5. The Abel theorem on the unsolvability in radicals of the general
quintic equation 140
§6.6. The Tschirnhaus transformations. Quintic equations in Bring s
form 145
Chapter 7. Theta Functions and Solutions of Quintic Equations 149
§7.1. Definition of theta functions 149
§7.2. Zeros of theta functions 150
§7.3. The relation O* = @* + 6^ 151
§7.4. Representation of theta functions by infinite products 152
§7.5. The relation 6i(0) = 7reo(0)e2(0)e3(0) 154
§7.6. Dedekind s // function and the functions /, /i, fi 155
§7.7. Transformations of theta functions induced by transformations
of r 156
§7.8. The general scheme of solution of quintic equations 158
§7.9. Transformations of order 5 159
§7.10. The change of parameter t i— r + 2 160
§7.11. The change of parameter rn i 161
§7.12. The change of parameter r i— ^~ 163
§7.13. Functions invariant with respect to the changes of parameter r h
T + 2,T^ fandTM^f 164
§7.14. Deduction of the modular equation 165
§7.15. Solving quintic equations 166
§7.16. The main modular function j(r) 169
§7.17. The fundamental domain of j(r) 170
§7.18. How to solve the equation j(r) = c 173
§7.19. The functions invariant under the changes of parameter tmt+1
and t m i 175
§7.20. The functions invariant with respect to the changes of parameter
rwT + 2andTM I 176
Bibliography 179
Index 183
|
| any_adam_object | 1 |
| author | Prasolov, Viktor V. 1956- Solov'ev, Jurij P. |
| author_GND | (DE-588)129271977 |
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| classification_tum | MAT 334f |
| ctrlnum | (OCoLC)37107130 (DE-599)BVBBV011951485 |
| dewey-full | 515/.983 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.983 |
| dewey-search | 515/.983 |
| dewey-sort | 3515 3983 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV011951485 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:03Z |
| institution | BVB |
| isbn | 0821805878 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008080177 |
| oclc_num | 37107130 |
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| owner_facet | DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 |
| physical | X, 185 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Prasolov, Viktor V. 1956- Verfasser (DE-588)129271977 aut Elliptičeskie funkcii i elliptičeskie integraly Elliptic functions and elliptic integrals Viktor Prasolov ; Yuri Solovyev Providence, RI American Math. Soc. 1997 X, 185 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 170 Aus dem Russ. übers. Fonctions elliptiques ram Elliptic functions Elliptisches Integral (DE-588)4152029-4 gnd rswk-swf Elliptische Funktion (DE-588)4134665-8 gnd rswk-swf Elliptische Funktion (DE-588)4134665-8 s DE-604 Elliptisches Integral (DE-588)4152029-4 s Solov'ev, Jurij P. Verfasser aut Translations of mathematical monographs 170 (DE-604)BV000002394 170 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008080177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prasolov, Viktor V. 1956- Solov'ev, Jurij P. Elliptic functions and elliptic integrals Translations of mathematical monographs Fonctions elliptiques ram Elliptic functions Elliptisches Integral (DE-588)4152029-4 gnd Elliptische Funktion (DE-588)4134665-8 gnd |
| subject_GND | (DE-588)4152029-4 (DE-588)4134665-8 |
| title | Elliptic functions and elliptic integrals |
| title_alt | Elliptičeskie funkcii i elliptičeskie integraly |
| title_auth | Elliptic functions and elliptic integrals |
| title_exact_search | Elliptic functions and elliptic integrals |
| title_full | Elliptic functions and elliptic integrals Viktor Prasolov ; Yuri Solovyev |
| title_fullStr | Elliptic functions and elliptic integrals Viktor Prasolov ; Yuri Solovyev |
| title_full_unstemmed | Elliptic functions and elliptic integrals Viktor Prasolov ; Yuri Solovyev |
| title_short | Elliptic functions and elliptic integrals |
| title_sort | elliptic functions and elliptic integrals |
| topic | Fonctions elliptiques ram Elliptic functions Elliptisches Integral (DE-588)4152029-4 gnd Elliptische Funktion (DE-588)4134665-8 gnd |
| topic_facet | Fonctions elliptiques Elliptic functions Elliptisches Integral Elliptische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008080177&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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