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arXiv · 1507.07975

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

Cormac O'Sullivan
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Abstract

The generating function for $p_N(n)$, the number of partitions of $n$ into at most $N$ parts, may be written as a product of $N$ factors. We find the behavior of coefficients in the partial fraction decomposition of this product as $N \to \infty$ 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.

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Cormac O'Sullivan. 2015-07-28. Asymptotics for the partial fractions of the restricted partition generating function I. https://arxiv.org/abs/1507.07975

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