Elliptic Curves
Function Theory, Geometry, Arithmetic
Seiten
2025
Cambridge University Press (Verlag)
978-1-009-60211-2 (ISBN)
Cambridge University Press (Verlag)
978-1-009-60211-2 (ISBN)
Reissued with a new Foreword, this book presents an introductory account of elliptical curves. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. An ideal introduction for graduate students and researchers in mathematics and physics, including exercises throughout.
The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.
The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.
Foreword: Preface; 1. First ideas: complex manifolds, Riemann surfaces, and projective curves; 2. Elliptic integrals and functions; 3. Theta functions; 4. Modular groups and modular functions; 5. Ikosaeder and the quintic; 6. Imaginary quadratic number fields; 7. Arithmetic of elliptic curves; References; Index.
| Erscheinungsdatum | 21.02.2025 |
|---|---|
| Reihe/Serie | Cambridge Mathematical Library |
| Vorwort | Alex Kasman |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 456 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-009-60211-X / 100960211X |
| ISBN-13 | 978-1-009-60211-2 / 9781009602112 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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