Advertisement

Table of contents

  1. Front Matter
    Pages i-xi
  2. General Theory

    1. Front Matter
      Pages 1-3
    2. Serge Lang
      Pages 5-21
    3. Serge Lang
      Pages 23-28
    4. Serge Lang
      Pages 29-41
    5. Serge Lang
      Pages 43-50
    6. Serge Lang
      Pages 51-59
    7. Serge Lang
      Pages 61-74
  3. Complex Multiplication Elliptic Curves with Singular Invariants

    1. Front Matter
      Pages 85-87
    2. Serge Lang
      Pages 89-109
    3. Serge Lang
      Pages 111-121
    4. Serge Lang
      Pages 123-147
    5. Serge Lang
      Pages 149-159
    6. Serge Lang
      Pages 161-170
    7. Serge Lang
      Pages 187-192
  4. Elliptic Curves with Non-Integral Invariants

    1. Front Matter
      Pages 193-195
    2. Serge Lang
      Pages 197-204
    3. Serge Lang
      Pages 205-220
    4. Serge Lang
      Pages 221-233
  5. Theta Functions and Kronecker Limit Formulas

    1. Front Matter
      Pages 235-237
    2. Serge Lang
      Pages 239-257
    3. Serge Lang
      Pages 259-266
    4. Serge Lang
      Pages 267-278
    5. Serge Lang
      Pages 279-285
    6. Serge Lang
      Pages 287-293
  6. Back Matter
    Pages 295-328

About this book

Introduction

Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points. The last part covers theta functions and the Kronecker Limit Formula. Also included is an appendix by Tate on algebraic formulas in arbitrary charactistic.

Keywords

Modular form complex analysis elliptic function integral operator theta function

Authors and affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4752-4
  • Copyright Information Springer-Verlag New York 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-9142-8
  • Online ISBN 978-1-4612-4752-4
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site