Band 231
Elliptic Curves Diophantine Analysis
Aus der Reihe
Grundlehren der mathematischen Wissenschaften
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- Hardcover
- Taschenbuch ausgewählt
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Sprache:Englisch
Fr. 137.00
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
19.10.2010
Abbildungen
XI, 264 p.
Verlag
Springer BerlinSeitenzahl
264
Maße (L/B/H)
23.5/15.5/1.6 cm
Gewicht
429 g
Auflage
Softcover reprint of the original 1st edition 1978
Sprache
Englisch
ISBN
978-3-642-05717-5
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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