An Asymptotic for the Partition Function

By Alexander Walker

March 12, 2014

Abstract

The partition function p(n) counts the number of ways a positive integer can be written as a sum of positive integers (order does not matter). The function p(n) was studied as early as Euler's time, but an asymptotic for the growth of p(n) remained elusive until 1918, when Hardy and Ramanujan developed the circle method. In this talk, I will provide a sketch of this first proof, and discuss a more recent attack on the problem grown out of weak Maass forms.