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1.

図書

図書
Helmut Hasse ; English translation edited and prepared for publication by Horst Günter Zimmer
出版情報: Berlin ; New York : Springer-Verlag, 1980  xvii, 638 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 229
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2.

図書

図書
editor, Horst G. Zimmer
出版情報: Berlin : Walter de Gruyter, c1996  xx, 201 p. ; ports. : 25 cm
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3.

図書

図書
Horst G. Zimmer
出版情報: Berlin : Springer-Verlag, 1972  103 p. ; 26 cm
シリーズ名: Lecture notes in mathematics ; 262
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4.

図書

図書
Susanne Schmitt, Horst G. Zimmer ; with an appendix by Attila Pethö
出版情報: Berlin ; New York : Walter de Gruyter, c2003  ix, 367 p. ; 25 cm
シリーズ名: De Gruyter studies in mathematics ; 31
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目次情報: 続きを見る
Preface
Elliptic curves / 1:
Normal forms / 1.1:
The addition law / 1.2:
Multiplication formulas / 1.3:
Factorization and primality test / 1.4:
Isogenies and endomorphisms of elliptic curves / 1.5:
Exercises / 1.6:
Elliptic curves over the complex numbers / 2:
Lattices / 2.1:
Weierstrass [Weierstrass p]-function / 2.2:
Periods of elliptic curves / 2.3:
Complex multiplication / 2.4:
Elliptic curves over finite fields / 2.5:
Frobenius endomorphism and supersingular curves / 3.1:
Computing the number of points / 3.2:
Construction of elliptic curves with given group order / 3.3:
Elliptic curves in cryptography / 3.4:
The discrete logarithm problem on elliptic curves / 3.5:
Elliptic curves over local fields / 3.6:
Reduction / 4.1:
The filtration / 4.2:
The theorem of Nagell, Lutz, and Cassels / 4.3:
The Mordell-Weil theorem and heights / 4.4:
Theorem of Mordell and Weil / 5.1:
Heights / 5.2:
Computation of the heights / 5.3:
Points of bounded height / 5.4:
The differences between the heights / 5.5:
Torsion group / 5.6:
Structure of the torsion group / 6.1:
Elliptic curves with integral j-invariant / 6.2:
Computation of the torsion group / 6.3:
Examples / 6.6:
The rank / 6.7:
L-series / 7.1:
The coefficients of the L-series / 7.2:
Continuation of the L-series / 7.3:
Conjectures concerning the rank / 7.4:
The Selmer and the Tate-Shafarevich group / 7.5:
2-descent / 7.6:
The rank in field extensions / 7.7:
Basis / 7.8:
Linearly independent points / 8.1:
Computation of a basis / 8.2:
Heegner point method / 8.3:
S-integral points / 8.5:
Overview / 9.1:
Elliptic logarithms / 9.2:
S-integral points over Q / 9.3:
Proof of the theorem / 9.4:
Example / 9.5:
Algorithmic theory of diophantine equations / 9.6:
Hilbert's 10th problem / A.1:
Introduction to Baker's method / A.2:
S-unit equations / A.3:
Thue equations / A.4:
Small collection of other results / A.5:
Lower bounds for linear forms in logarithms / A.6:
LLL-algorithm / A.7:
Reduction of the large bound / A.8:
Multiquadratic number fields / B:
Multiquadratic fields and Galois groups / B.1:
Discriminants / B.2:
Integral Bases / B.3:
Decomposition Law / B.4:
Biquadratic number fields / B.5:
Totally real and totally complex biquadratic fields / B.6:
Bibliography / B.7:
Index
Preface
Elliptic curves / 1:
Normal forms / 1.1:
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