Modular Symbols
Slide 2
Motivation
Birch and Swinnerton-Dyer
The BSD Conjecture
Birch introduced modular symbols
How can we compute in the modular world?
Subgroups of the modular group
Modular Curves
Modular curve for N=3:
Modular curve X (37):
Modular Forms
Examples of modular forms
Computing the space of modular symbols
Explicit presentation of modular symbols
Relations
Example: N=11
Manins Trick
Slide 20
Slide 21
The connection with modular forms
Example
Applications of Modular Symbols
Key References and Software
Author: William Stein
E-mail: [email protected]
Homepage: http://www.math.harvard.edu/~was