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.References
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Additional Information
- Michael Drmota
- Affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10/105-1, A-1040 Vienna, Austria
- MR Author ID: 59890
- Email: michael.drmota@tuwien.ac.at
- Stefan Gerhold
- Affiliation: Institute of Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8–10/105-1, A-1040 Vienna, Austria
- MR Author ID: 751967
- Email: sgerhold@fam.tuwien.ac.at
- Received by editor(s): December 16, 2013
- Received by editor(s) in revised form: June 12, 2014
- Published electronically: November 21, 2014
- Additional Notes: The authors gratefully acknowledge financial support from the Austrian Science Fund (FWF) under grants P 24880-N25 (second author), resp. F5002 (first author).
- Communicated by: Matthew A. Papanikolas
- © Copyright 2014 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 121-134
- MSC (2010): Primary 11P82, 41A60
- DOI: https://doi.org/10.1090/S2330-1511-2014-00014-6
- MathSciNet review: 3280294