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- Title
Asymptotics for the partial fractions of the restricted partition generating function I.
- Authors
O'Sullivan, Cormac
- Abstract
The generating function for , the number of partitions of into at most parts, may be written as a product of factors. We find the behavior of coefficients in the partial fraction decomposition of this product as 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.
- Subjects
PARTIAL fractions; PARTITION functions; MATHEMATICAL decomposition; DILOGARITHMS; SADDLEPOINT approximations
- Publication
International Journal of Number Theory, 2016, Vol 12, Issue 6, p1421
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042116500895