S Lang

(Author)

Elliptic Curves: Diophantine Analysis (1978)Hardcover - 1978, 1 November 1978

Elliptic Curves: Diophantine Analysis (1978)
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Part of Series
Grundlehren Der Mathematischen Wissenschaften
Part of Series
Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover)
Print Length
264 pages
Language
English
Publisher
Springer
Date Published
1 Nov 1978
ISBN-10
3540084894
ISBN-13
9783540084891

Description

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.

Product Details

Author:
S Lang
Book Edition:
1978
Book Format:
Hardcover
Country of Origin:
US
Date Published:
1 November 1978
Dimensions:
23.39 x 15.6 x 1.75 cm
ISBN-10:
3540084894
ISBN-13:
9783540084891
Language:
English
Location:
Berlin, Heidelberg
Pages:
264
Publisher:
Weight:
566.99 gm

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