The Ramanujan Journal

, Volume 18, Issue 1, pp 113–119 | Cite as

Simple upper bounds for partition functions

Article

Abstract

We tweak Siegel’s method to produce a rather simple proof of a new upper bound on the number of partitions of an integer into an exact number of parts. Our approach, which exploits the delightful dilogarithm function, extends easily to numerous other counting functions.

Keywords

Partitions Dilogarithm 

Mathematics Subject Classification (2000)

11P81 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematics, College of Staten IslandCUNYStaten IslandUSA

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