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Real Elliptic Curves

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Author(s): Norman L. Alling (Eds.)
Series: North-Holland Mathematics Studies 54
Publisher: Elsevier, Academic Press
Year: 1981

Language: English
Pages: iii-viii, 1-349

Content:
Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages vii-viii
Norman L. Ailing

Chapter 0 Introduction
Pages 1-8

Chapter 1 Examples of Elliptic Integrals
Pages 11-20

Chapter 2 Some Addition Theorems
Pages 21-31

Chapter 3 Development of Some Discoveries Made Prior to 1827
Pages 33-55

Chapter 4 Inverting the Integral
Pages 59-74

Chapter 5 Theta Functions
Pages 75-84

Chapter 6 The Introduction of Analytic Function Theory
Pages 85-101

Chapter 7 Weierstrass's Work on Elliptic Functions
Pages 103-133

Chapter 8 Riemann Surfaces
Pages 135-165

Chapter 9 The Elliptic Modular Function
Pages 167-187

Chapter 10 Algebraic Function Fields
Pages 189-204

Chapter 11 Real Algebraic Function Fields and Compact Klein Surfaces
Pages 207-215

Chapter 12 The Species and Geometric Moduli of a Real Elliptic Curve
Pages 217-236

Chapter 13 Automorphisms of Real Elliptic Curves
Pages 237-249

Chapter 14 From Species and Geometric Moduli to Defining Equations
Pages 251-271

Chapter 15 The Divisor Class Group of Ys,t
Pages 273-281

Chapter 16 Analytic Differentials
Pages 283-288

Chapter 17 From Defining Equation to Species and Moduli
Pages 289-333

Bibliography
Pages 335-339

Index
Pages 341-349