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Grundlehren der mathematischen Wissenschaften

Elliptic Curves

Diophantine Analysis

Authors: Lang, S.

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About this book

It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-3-662-07010-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
Softcover $99.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Elliptic Curves
Book Subtitle
Diophantine Analysis
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
231
Copyright
1978
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-07010-9
DOI
10.1007/978-3-662-07010-9
Hardcover ISBN
978-3-540-08489-1
Softcover ISBN
978-3-642-05717-5
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XI, 264
Topics

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