Elliptic Curves And Modular Forms by Robert C. Rhoades
File Type :PDF Number of Pages :142
Description This note is an introduction to
elliptic curves and modular forms. These play a central
role in modern arithmetical geometry and even in applications to cryptography.
On the elliptic curve side, we shall cover elliptic curves over finite fields,
over the complex numbers, and over the rationals. Topics covered includes:
Congruent Numbers, Hasse Principal, Elliptic Curves over C, Riemann Surfaces,
Addition Law, Explicit Group Law, Modular Forms and Modular Curves, Elliptic
Curves over Finite Fields, Dual Isogeny, Dichotomy Between Super-Singular and
Ordinary Case, Mordell’s Theorem.
|