Disproof of a conjecture by Rademacher on partial fractions

@article{Drmota2013DisproofOA,
title={Disproof of a conjecture by Rademacher on partial fractions},
author={Michael Drmota and S. Gerhold},
journal={arXiv: Number Theory},
year={2013}
}

In his book Topics in Analytic Number Theory, Rademacher considered the generating function of partitions into at most $N$ parts, and conjectured certain limits for the coefficients of its partial fraction decomposition. We carry out an asymptotic analysis that disproves this conjecture, thus confirming recent observations of Sills and Zeilberger (Journal of Difference Equations and Applications 19, 2013), who gave strong numerical evidence against the conjecture.