Math 662 (Section 602) -- Spring 2005

Seminar in Algebra:
Introduction to Modular Forms

Tuesday & Thursday 2:20-3:35


Course Description:

This course will be an introduction to modular forms and their powerful applications to number theory. We will start from the beginning; only the fundamentals of number theory of the integers and some complex analysis will be assumed. The course will cover the following topics:
  • Riemann zeta-function and Dirichlet L-functions
  • elliptic functions and elliptic curves
  • SL_2(Z) and congruence subgroups
  • quotients of the upper half-plane and cusps
  • modular forms and modular functions
  • Fourier expansions of modular forms
  • Hecke operators
  • L-functions of modular forms

Course Information:

Instructor: Dr. Matthew Papanikolas

Office Hours: TBA

Office: 321 Milner

Office Phone: 845-1615


Textbook: Introduction to Elliptic Curves and Modular Forms, 2nd ed., by Neal Koblitz, Springer-Verlag, GTM 97.

Prerequisites: Math 627 (Number Theory) and Math 407 or 617 (Complex Analysis); or equivalents

Course Webpage:

Course Work and Grades: There will be regular homework assignments as well as a final project at the end of the semester. These will serve as the basis for grades in the course.

Page maintained by Matt Papanikolas, Dept. of Mathematics, Texas A&M University.