Notes on "Quadratic Forms and Automorphic Forms" from the 2009 Arizona Winter School

TL;DR

This paper provides a survey of quadratic forms over number fields and their links to modular and automorphic forms, based on a graduate course at the 2009 Arizona Winter School.

Contribution

It offers an extended, accessible overview of classical quadratic forms and their automorphic connections, tailored for graduate-level understanding.

Findings

Survey of quadratic forms over Q and Z

Explanation of connections with modular forms

Overview of automorphic forms related to quadratic forms

Abstract

These notes are an extension of the rough notes provided for my four lecture graduate level course on "Quadratic Forms and Automorphic Forms" at the March 2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey of some aspects of the classical theory of quadratic forms over number fields and their rings of integers (e.g. over Q and Z), and their connection with modular and automorphic forms.