1. Introduction

In his book Topics in Analytic Number Theory Reference 13, Hans Rademacher gave a partial fraction decomposition of the partition generating function $\prod _{j\geq 1}(1-x^j)^{-1}$. He conjectured that the decomposition of the generating function of partitions into at most $N$ parts (equivalently, into parts from $\{1,\dots ,N\}$),

End of introduction