Elliptic Curves: Diophantine Analysis

Lang, Serge

Published by Springer-Verlag, 1978
ISBN 10: 0387084894 / ISBN 13: 9780387084893
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Synopsis: 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.

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Title: Elliptic Curves: Diophantine Analysis
Publisher: Springer-Verlag
Publication Date: 1978
Binding: Hardcover
Book Condition: Good

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Lang, Serge
Published by Springer-Verlag, Berlin (1978)
ISBN 10: 0387084894 ISBN 13: 9780387084893
Used Hardcover Quantity Available: 1
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Book Description Springer-Verlag, Berlin, 1978. Hard Cover. Book Condition: Fine. A very clean, unmarked copy. Bookseller Inventory # 00036278

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