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Acta Mathematica Hungarica
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Asymptotic Density and the Asymptotics of Partition Functions

Asymptotic density and the asymptotics of partition functions
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2000Embargo end date: 01 Jan 2000 English Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Hungarica, volume 87, pages 179-195 (issn: 0236-5294, eissn: 1588-2632, Copyright policy )
Authors: Melvyn B. Nathanson;

doi: 10.1023/a:1006789419031 , 10.48550/arxiv.math/0002103

arXiv: http://arxiv.org/abs/math/0002103

Asymptotic Density and the Asymptotics of Partition Functions

Abstract

Let A be a set of positive integers with gcd(A) = 1, and let p_A(n) be the partition function of A. Let c = ��\sqrt(2/3). Let ��> 0. It is proved that log p_A(n) ~ c\sqrt(��n) if and only if the set A has asymptotic density ��.

17 pages. To appear in Acta Math. Hungarica

Related Organizations
Keywords

Mathematics - Number Theory, FOS: Mathematics, Mathematics - Combinatorics, Analytic theory of partitions, Number Theory (math.NT), Combinatorics (math.CO), 11P82,11P70,11B05, asymptotic density, partition functions

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
Average
Green