Class Number One Problems

In this paper we examine some of the developments concerning the Gauss class number problems and build a solid understanding of the class number. First we will develop some background knowledge necessary to understand the problem, specifically the theory of quadratic forms and quadratic fields and how the class number is represented in each. The current form of Gauss' conjectures will not be formally stated until this groundwork is set. The class equation will then be thoroughly examined in order to illustrate the connection between the class number and L-functions