The partial fraction decomposition of the restricted partition generating function and Rademacher's conjecture.

The generating function for the partitions of an integer m into at most N parts may be written as a simple product. Rademacher studied the coefficients of the partial fraction decomposition of this product and made a conjecture in 1973 for the limits of these coefficients as N goes to infinity based on his famous exact formula for the unrestricted partitions. This talk describes the latest results on Rademacher's conjecture and connections with the zeros of the dilogarithm function.

Cormac O'Sullivan