O’Sullivan, Cormac Asymptotics for the partial fractions of the restricted partition generating function. II. (English) Zbl 1386.11112 Integers 16, Paper A78, 73 p. (2016). 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. Cited in 3 Documents MSC: 11P82 Analytic theory of partitions 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) Keywords:restricted partitions; partial fraction decomposition; saddle-point method; dilogarithm Citations:Zbl 1407.11119 Software:HANS PDFBibTeX XMLCite \textit{C. O'Sullivan}, Integers 16, Paper A78, 73 p. (2016; Zbl 1386.11112) Full Text: arXiv EMIS