Introduction to Elliptic Curves and Modular FormsNew York, 1984 - 248 pages The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves. |
Table des matières
CHAPTER | 1 |
Doubly periodic functions | 14 |
Elliptic curves in Weierstrass form | 22 |
Droits d'auteur | |
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Expressions et termes fréquents
a₁ algebraic b₁ change of variables character modulo completes the proof compute congruence subgroup constant converges corresponding cusp form define definition denote Dirichlet character double coset E₂(z eigenform Eisenstein series elements elliptic curve elliptic curve y² equal Euler product example factor finite fixed follows form of weight formula functional equation fundamental domain gives Hasse-Weil L-function Hecke operators holomorphic inner sum isomorphism L-series L(XD lattice Lemma linear m₁ M₁(N matrix modular forms modular function modular points modulo multiple n₁ n²x nontrivial nonzero obtain P₁ points of order pole polynomial positive integer prime proof of Proposition Prove q-expansion q-expansion coefficients rational replace right coset root satisfies Shimura map SL₂(Z square squarefree suppose theorem trivial Tunnell's w₁ w₂ y₁ Z/NZ z₁ zero zeta-function