William Stein
Date: Math 124 HARVARD UNIVERSITY Fall 2001
Recall that a binary quadratic form is a function . Our motivating problem is to decide which numbers are ``represented'' by ; i.e., for which integers do there exist integers such that ? If then and represent exactly the same set of integers. Also, , where , and is called positive definite if and .In today's lecture, we will learn about reduction theory, which allows us to decide whether or not two positive definite binary quadratic forms are equivalent under the action of .
If, in the future, you would like to pursue the theory of binary quadratic forms in either a more algebraic or algorithmic direction, I highly recommend that you look at Chapter 5 of Henri Cohen's book A Course in Computational Algebraic Number Theory (GTM 138).