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Elliptic Curves

  • Textbook
  • © 1987

Overview

Authors:
  1. Dale Husemöller

    1. Department of Mathematics, Haverford College, Haverford, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 111)

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XV
    Download chapter PDF

  2. Introduction to Rational Points on Plane Curves

    • Dale Husemöller
    Pages 1-21

  3. Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve

    • Dale Husemöller
    Pages 22-42

  4. Plane Algebraic Curves

    • Dale Husemöller
    Pages 43-61

  5. Elliptic Curves and Their Isomorphisms

    • Dale Husemöller
    Pages 62-80

  6. Families of Elliptic Curves and Geometric Properties of Torsion Points

    • Dale Husemöller
    Pages 81-98

  7. Reduction mod p and Torsion Points

    • Dale Husemöller
    Pages 99-119

  8. Proof of Mordell’s Finite Generation Theorem

    • Dale Husemöller
    Pages 120-137

  9. Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields

    • Dale Husemöller
    Pages 138-151

  10. Descent and Galois Cohomology

    • Dale Husemöller
    Pages 152-161

  11. Elliptic and Hypergeometric Functions

    • Dale Husemöller
    Pages 162-182

  12. Theta Functions

    • Dale Husemöller
    Pages 183-201

  13. Modular Functions

    • Dale Husemöller
    Pages 202-221

  14. Endomorphisms of Elliptic Curves

    • Dale Husemöller
    Pages 222-241

  15. Elliptic Curves over Finite Fields

    • Dale Husemöller
    Pages 242-261

  16. Elliptic Curves over Local Fields

    • Dale Husemöller
    Pages 262-271

  17. Elliptic Curves over Global Fields and ℓ-Adic Representations

    • Dale Husemöller
    Pages 272-289

  18. L-Function of an Elliptic Curve and Its Analytic Continuation

    • Dale Husemöller
    Pages 290-305

  19. Remarks on the Birch and Swinnerton-Dyer Conjecture

    • Dale Husemöller
    Pages 306-314

  20. Back Matter

    Pages 315-350
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Keywords

About this book

The book divides naturally into several parts according to the level of the material, the background required of the reader, and the style of presentation with respect to details of proofs. For example, the first part, to Chapter 6, is undergraduate in level, the second part requires a background in Galois theory and the third some complex analysis, while the last parts, from Chapter 12 on, are mostly at graduate level. A general outline ofmuch ofthe material can be found in Tate's colloquium lectures reproduced as an article in Inven­ tiones [1974]. The first part grew out of Tate's 1961 Haverford Philips Lectures as an attempt to write something for publication c10sely related to the original Tate notes which were more or less taken from the tape recording of the lectures themselves. This inc1udes parts of the Introduction and the first six chapters The aim ofthis part is to prove, by elementary methods, the Mordell theorem on the finite generation of the rational points on elliptic curves defined over the rational numbers. In 1970 Tate teturned to Haverford to give again, in revised form, the originallectures of 1961 and to extend the material so that it would be suitable for publication. This led to a broader plan forthe book.

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)

Authors and Affiliations

  • Department of Mathematics, Haverford College, Haverford, USA

    Dale Husemöller

Bibliographic Information

  • Book Title: Elliptic Curves

  • Authors: Dale Husemöller

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-5119-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1987

  • eBook ISBN: 978-1-4757-5119-2Published: 29 June 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XV, 350

  • Topics: Analysis

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