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Asymptotics for the partial fractions of the restricted partition generating function. II. (English) Zbl 1386.11112

Summary: 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. In an earlier paper [Int. J. Number Theory 12, No. 6, 1421–1474 (2016; Zbl 1407.11119)], we studied the behavior of coefficients in the partial fraction decomposition of this product as \(N \rightarrow \infty\) by applying the saddle-point method to get the asymptotics of the main terms. In this paper, we bound the error terms. This involves estimating products of sines and further saddle-point arguments. The saddle-points needed are associated with zeros of the analytically continued dilogarithm.

MSC:

11P82 Analytic theory of partitions
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)

Citations:

Zbl 1407.11119

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