TY  - BOOK
AU  - Lang, Serge
TI  - Elliptic curves : : diophantine analysis
T2  - Grundlehren der mathematischen Wissenschaften
SN  - 9783642057175
U1  - 512.742 
PY  - 1978///
CY  - New York
PB  - Springer-Verlag
KW  - Diophantine analysis
KW  - Curves, Elliptic
KW  - Algebra
KW  - Arithmetic
KW  - Curves
KW  - Diophantische Approximation
KW  - Diophantische Ungleichung
KW  - Elliptische Kurve
KW  - Function
KW  - Theorem
N1  - Includes index; Bibliography: p. [253]-259
N2  - 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
UR  - https://link.springer.com/book/10.1007/978-3-662-07010-9#toc
UR  - https://www.goodreads.com/book/show/14632103-elliptic-curves?ref=nav_sb_ss_1_13#CommunityReviews
ER  -