عنوان

Elliptic Curves :

(Number (ISBN

3662070103

(Number (ISBN

9783662070109

Number

b579719

Title Proper

Elliptic Curves :

General Material Designation

[Book]

Other Title Information

Diophantine Analysis

First Statement of Responsibility

by Serge Lang.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg : Imprint : Springer

Date of Publication, Distribution, etc.

1978

Specific Material Designation and Extent of Item

(XII, 264 pages)

Series Title

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 231.

Text of Note

I. General Algebraic Theory --; I. Elliptic Functions --; II. The Division Equation --; III. p-Adic Addition --; IV. Heights --; V. Kummer Theory --; V1. Integral Points --; II. Approximation of Logarithms --; VII. Auxiliary Results --; VIII. The Baker--Feldman Theorem --; IX. Linear Combinations of Elliptic Logarithms --; X. The Baker--Tijdeman Theorem --; XI. Refined Inequalities.

Text of Note

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.

Analyse diophantienne.

Courbes elliptiques.

Global analysis (Mathematics)

by Serge Lang.

Serge Lang

Electronic name

[Book]

Y