حدس بیرچ و سوینرتون-دایر: رویکرد محاسباتی

Preface Chapter 1. The BSD Rank Conjecture 1.1. Statement of the BSD Rank Conjecture 1.2. The BSD Rank Conjecture Implies that E(Q) is Computable 1.3. The Complex L-series L(E,s) 1.4. Computing L(E,s) 1.5. The p-adic L-series 1.6. Computing Lp(E,T) Chapter 2. The Birch and Swinnerton-Dyer Formula 2.1. Galois Cohomology 2.2. The Shafarevich-Tate Group 2.3. The Birch and Swinnerton-Dyer Formula 2.4. Examples: The Birch and Swinnerton-Dyer Formula 2.5. The p-adic BSD Conjectural Formula Chapter 3. Heegner Points and Kolyvagin's Euler System 3.1. CM Elliptic Curves 3.2. Heegner Points 3.3. Computing Heegner Points 3.4. Kolyvagin's Euler System 3.5. The Gross-Zagier Theorem Chapter 4. Computational Verification of the Conjecture 4.1. Theorem 4.2. Examples Bibliography