Disproof of a conjecture by Rademacher on partial fractions

Drmota, Michael; Gerhold, Stefan

doi:10.1090/S2330-1511-2014-00014-6

Disproof of a conjecture by Rademacher on partial fractions
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by Michael Drmota and Stefan Gerhold HTML | PDF

Proc. Amer. Math. Soc. Ser. B 1 (2014), 121-134

Abstract:

In his book Topics in Analytic Number Theory (1973), Hans Rademacher considered the generating function of integer partitions into at most $N$ parts and conjectured certain limits for the coefficients of its partial fraction decomposition. We carry out an asymptotic analysis that disproves this conjecture, thus confirming recent observations of Sills and Zeilberger (Journal of Difference Equations and Applications 19 (2013)), who gave strong numerical evidence against the conjecture.

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