The asymptotic distribution of Andrews' smallest parts function
type: Item
instance of: scholarly article
title: The asymptotic distribution of Andrews' smallest parts function
zbMATH Open document ID: 1332.11092
author: Josiah Banks
author: Adrian Barquero-Sanchez
author: Riad Masri
author: Yan Sheng
published in: Archiv der Mathematik
publication date: 2015-12-11T00:00:00Z
full work available at URL: http://hdl.handle.net/10669/76492
review text: The smallest parts function \(spt(n)\) was defined by \textit{G. E. Andrews} in [J. Reine Angew. Math. 624, 133--142 (2008; Zbl 1153.11053)] and counts the number of smallest parts associated to partitions of the positive integer \(n\). This function has interesting properties and satisfies congruences similar to Ramanujan's congruences for the partition function \(p(n)\). In this paper, using methods from spectral theory of automorphic forms, the authors give an asymptotic formula with a power saving error for the function \(spt(n)\). The main application is a similar formula for the number of \(2\)-marked Durfee symbols associated to partitions of \(n\).
reviewed by: Mircea Merca
Mathematics Subject Classification ID: 11P82
Mathematics Subject Classification ID: 11P81
zbMATH DE Number: 6520101
zbMATH Keywords: Durfee symbol
zbMATH Keywords: partition
zbMATH Keywords: smallest parts function
MaRDI profile type: Publication
OpenAlex ID: W1956209209
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DOI: 10.1007/S00013-015-0831-9
description: scientific article; zbMATH DE number 6520101