Modular Forms:

A Classical Introduction

Welcome to the webpage for my lecture notes on modular forms, first drafted for a Spring 2011 course at the University of Oklahoma.

I periodically update these notes, so please contact me with any errors you find.

Here is a brief table of contents. I hope to continue (slowly) adding to these notes, but at present some of the later chapters are less complete than the earlier ones.

Part I (Basic course)

  1. Introduction
  2. Elliptic functions
  3. The Poincare upper half-plane
  4. Modular forms
  5. Dimensions of spaces of modular forms
  6. Hecke operators
  7. L-functions
Part II (Selected topics)
  1. Newforms and oldforms
  2. Hilbert modular forms
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