Elliptic Curves: Diophantine Analysis: 231 (Grundlehren der mathematischen Wissenschaften) - Tapa dura

Lang, S.

 
9783540084891: Elliptic Curves: Diophantine Analysis: 231 (Grundlehren der mathematischen Wissenschaften)
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ISBN 10: 3540084894 ISBN 13: 9783540084891
Editorial: Springer, 1978

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

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.

Reseña del editor

This book takes the view that parallel to the pure arithmetic theory over number fields lies the algebraic-geometric theory of algebraic systems, where sections play the role of rational points. The author formulates analogs of classic diophantine problems.

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Editorial
Springer
Año de publicación
1978
Idioma
Inglés
ISBN 10 
3540084894
ISBN 13 
9783540084891
Encuadernación
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Número de páginas
280
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
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Friedrich-Karl-Str. 9
Hamburg
Alemania

Otras ediciones populares con el mismo título

9783642057175: Elliptic Curves: Diophantine Analysis: 231 (Grundlehren der mathematischen Wissenschaften)

Edición Destacada

ISBN 10:  3642057179 ISBN 13:  9783642057175
Editorial: Springer, 2010
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