Asymptotics for the partial fractions of the restricted partition generating function I

Abstract

The generating function for [Formula: see text], the number of partitions of [Formula: see text] into at most [Formula: see text] parts, may be written as a product of [Formula: see text] factors. We find the behavior of coefficients in the partial fraction decomposition of this product as [Formula: see text] by applying the saddle-point method, where the saddle-point we need is associated to a zero of the analytically continued dilogarithm. Our main result disproves a conjecture of Rademacher.