Simple upper bounds for partition functions
type: Item
instance of: scholarly article
title: Simple upper bounds for partition functions
zbMATH Open document ID: 1195.11138
author: Wladimir de Azevedo Pribitkin
published in: The Ramanujan Journal
publication date: 2009-11-23T00:00:00Z
review text: The author proves the following Theorem: Let \(p_k(n)\) denote the number of partitions of \(n\) with exactly \(k\) parts. There exists an absolute constant \(A<1\) such that for \(k<n\) \[ p_k(n)<A\frac{e^{c\sqrt{n-k}}}{(n-k)^{3/4}}e^{-\frac{2\sqrt{n-k}}{c}\text{Li}_2(e^{-\frac{c(k+1/2)}{2\sqrt{n-k}}})}, \] where \(\text{Li}_2(x)=\sum_{m=1}^\infty\frac{x^m}{m^2}\), \(|x|\leq 1\), is the dilogarithm function, and \(c=\pi\sqrt{2/3}\).
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11P82
zbMATH DE Number: 5636932
zbMATH Keywords: partition function
zbMATH Keywords: upper bound
MaRDI profile type: Publication
full work available at URL: s11139-007-9022-z
OpenAlex ID: W2077614283
cites work: Q4218535
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DOI: 10.1007/S11139-007-9022-Z
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description: scientific article; zbMATH DE number 5636932