Modular Symbols

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Table of contents

Modular Symbols

Slide 2


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

Modular Symbols

Computing the space of modular symbols

Explicit presentation of modular symbols


Example: N=11

Manins Trick

Slide 20

Slide 21

The connection with modular forms


Applications of Modular Symbols

Key References and Software

Author: William Stein

E-mail: [email protected]