Rademacher’s series for the partition function

Thursday, April 28, 2016 - 11:00am
117 MSB
Alexandra Archer (Advisor: Prof William Banks)

In this talk, we will give a proof of Racemacher’s exact formula for p(n), the unrestricted partition function, which counts the number of ways a positive integer n can be expressed as a sum of positive integers.  We will introduce the notions of Farey sequences, Ford circles, and the Rademacher path, as well as several of their properties.  With the Rademacher path as the path of integration in the tau-plane, we will use several estimations to arrive at the formula for p(n), considered a “crowning achievement" of the ‘circle method’ of Hardy, Ramanujan, and Littlewood.