Introduction to Modular Forms 0366-5012-01

Prof. Zeev Rudnick

Tel Aviv, Spring 2018/2019

The course will cover the basic theory of modular forms, as well as some of their applications in number theory.

Contents:

The course will be given in English

Prerequisites

I will assume knowledge of the courses: complex function theory 1 and Introduction to number theory. The course Algebra B1 (basic group theory) will also be useful.

Notes

  1. Lattices
  2. Binary quadratic forms
  3. Elliptic functions
  4. Fourier coefficients I
  5. Fourier coefficients II: Petersson's formula
  6. Theta functions
  7. Hecke operators

Bibliography

Schedule

Sunday 13-16, Orenstein 102

Attendance is mandatory for people wanting a grade

Homework

There will be periodic homework assignments which are mandatory. The final grade will be based on the homework grades, class participation and a take-home exam.

Assignments

  1. Assignment 1, due date March 17, 2019
  2. Assignment 2, due date March 31, 2019
  3. Assignment 3, due date April 14, 2019
  4. Assignment 4, due date May 12, 2019
  5. Assignment 5, due date May 19, 2019

Contact me at: rudnick@tauex.tau.ac.il, Office : Schreiber 316, tel: 640-7806

Course homepage: http://www.math.tau.ac.il/~rudnick/courses/modular forms 2019/modular forms 2019.html