Introduction to Modular Forms 0366501201
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

Dirichlet series and Euler products
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 1316, 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 takehome 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

Final assignment, due date June 26, 2019
Contact me at: rudnick@tauex.tau.ac.il, Office : Schreiber 316, tel: 6407806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/modular forms 2019/modular forms 2019.html