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Graduate Texts in Mathematics

Elliptic Curves

Authors: Husemöller, Dale

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eBook 56,99 €
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  • ISBN 978-0-387-21577-8
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Hardcover 69,63 €
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  • ISBN 978-0-387-95490-5
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Softcover 69,63 €
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  • ISBN 978-1-4419-3025-5
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About this Textbook

This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer.

This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory.

About the First Edition:

"All in all the book is well written, and can serve as basis for a student seminar on the subject."

-G. Faltings, Zentralblatt

Reviews

From the reviews of the second edition:

"Husemöller’s text was and is the great first introduction to the world of elliptic curves … and a good guide to the current research literature as well. … this second edition builds on the original in several ways. … it has certainly gained a good deal of topicality, appeal, power of inspiration, and educational value for a wider public. No doubt, this text will maintain its role as both a useful primer and a passionate invitation to the evergreen theory of elliptic curves and their applications" (Werner Kleinert, Zentralblatt MATH, Vol. 1040, 2004)


Table of contents (21 chapters)

  • Introduction to Rational Points on Plane Curves

    Pages 1-22

    Preview Buy Chapter 30,19 €
  • Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve

    Pages 23-43

    Preview Buy Chapter 30,19 €
  • Plane Algebraic Curves

    Pages 45-63

    Preview Buy Chapter 30,19 €
  • Elliptic Curves and Their Isomorphisms

    Pages 65-84

    Preview Buy Chapter 30,19 €
  • Families of Elliptic Curves and Geometric Properties of Torsion Points

    Pages 85-102

    Preview Buy Chapter 30,19 €

Buy this book

eBook 56,99 €
price for Spain (gross)
  • ISBN 978-0-387-21577-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 69,63 €
price for Spain (gross)
  • ISBN 978-0-387-95490-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 69,63 €
price for Spain (gross)
  • ISBN 978-1-4419-3025-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Elliptic Curves
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
111
Copyright
2004
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-21577-8
DOI
10.1007/b97292
Hardcover ISBN
978-0-387-95490-5
Softcover ISBN
978-1-4419-3025-5
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XXII, 490
Topics