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Bibliographic Details
Main Authors:	Prasolov, Viktor V. 1956- (Author), Solov'ev, Jurij P. (Author)
Format:	Book
Language:	English Russian
Published:	Providence, RI American Math. Soc. 1997
Series:	Translations of mathematical monographs 170
Subjects:	Fonctions elliptiques Elliptic functions Elliptisches Integral Elliptische Funktion
Links:	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
Item Description:	Aus dem Russ. übers.
Physical Description:	X, 185 S. graph. Darst.
ISBN:	0821805878

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Record in the Search Index

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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
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indexdate	2024-12-20T10:21:35Z
institution	BVB
isbn	0821805878
language	English Russian
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-008080177
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physical	X, 185 S. graph. Darst.
publishDate	1997
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publisher	American Math. Soc.
record_format	marc
series	Translations of mathematical monographs
series2	Translations of mathematical monographs
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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