## Introduction to Modular Forms 0366.4390.01

## Prof. Zeev Rudnick

### Tel Aviv, Spring 2002/2003

The course is intended for third year undergraduates
or graduate students.
It will cover the basic theory of modular forms, as well as some
of their applications in number theory.
### Contents:

- The modular group and its subgroups
- Elliptic functions
- Eisenstein series
- Modular forms - basic properties
- Hecke operators
- Dirichlet series attached to modular forms
- Theta functions and quadratic forms
- Maass waveforms

### Prerequisites

I will assume knowledge of the courses:
complex function theory 1 and Introduction to number theory.
### Bibliography

- T. Apostol, Modular functions and Dirichlet series in Number Theory
- H. Iwaniec, Topics in classical automorphic forms
- N. Koblitz, Introduction to elliptic curves and modular forms
- J.-P. Serre, A Course in Arithmetic

## Schedule

Tuesday 10-13, Orenstein 110

## Homework

There will be periodic homework assignments which are
**mandatory**. 15% of the final grade will be based on the homework grades.

Contact me at: rudnick@post.tau.ac.il, Office : Schreiber 316, tel: 640-7806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/modular.html