As indicated by the title The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms, this paper leads us to an understanding of the relationship between these three areas of study. In [4], Zagier gives the results of an intriguing example of the relationship between these areas. However there...
The first published notion that the j-function was in any way related to the Monster came in 1979, when Conway and Norton noted in [CN79] that each coefficient in the q- expansion of the j-function could be written as a (nontrivial) integral linear combination of the dimensions of irreducible representations...
Just as prime numbers can be thought of as the building blocks of the natural numbers, in a similar fashion, simple groups may be considered the building blocks of finite groups. Burnside considered the following
questions:
1. Do there exist non-abelian simple groups of odd order?
2. Do there exist...
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...
The study into specific properties of the partition function has been a rich topic for number theorists for many years. Much of the current work involving the arithmetic properties of the partition function and their seed in some keen observations of Ramanujan.In particular he discovered what are referred to as...