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 space of lattices
- Binary quadratic forms
- The modular group and its subgroups
- Elliptic functions
- Eisenstein series
- Modular forms - basic properties
- Zeros of modular forms
- Fourier coefficients
- The Petersson inner product
- Hecke operators
- Dirichlet series attached to modular forms
- Theta functions and quadratic forms
- Maass waveforms
- Representation theoretic interpretation, GL(2) over the adeles (time permitting).
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
- Lattices
- Binary quadratic forms
-
Elliptic functions
-
Fourier coefficients I
-
Fourier coefficients II: Petersson's formula
-
Theta functions
-
Hecke operators
Bibliography
- H. Iwaniec, Topics in classical automorphic forms
- N. Koblitz, Introduction to elliptic curves and modular forms
- J.-P. Serre, A Course in Arithmetic
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
-
Assignment 1, due date March 17, 2019
-
Assignment 2, due date March 31, 2019
-
Assignment 3, due date April 14, 2019
-
Assignment 4, due date May 12, 2019
-
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