Conics - a Poor Man’s Elliptic Curves
نویسنده
چکیده
Introduction 2 1. The Group Law on Pell Conics and Elliptic Curves 2 1.1. Group Law on Conics 2 1.2. Group Law on Elliptic curves 3 2. The Group Structure 3 2.1. Finite Fields 3 2.2. p-adic Numbers 3 2.3. Integral and Rational Points 4 3. Applications 4 3.1. Primality Tests 4 3.2. Factorization Methods 5 4. 2-Descent 5 4.1. Selmer and Tate-Shafarevich Group 5 4.2. Heights 6 5. Analytic Methods 6 5.1. Zeta Functions 6 5.2. L-Functions for Conics 7 5.3. L-Functions for Elliptic Curves 8 6. Birch–Swinnerton-Dyer 8 6.1. Birch and Swinnerton-Dyer for Elliptic Curves 8 6.2. Birch and Swinnerton-Dyer for Conics 8 7. Summary 9 8. Questions 10 Acknowledgments 10 References 10
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