Asymptotic inequalities for k-ranks and their cumulation functions

Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bringmann and K. Mahlburg recently. Motivated by their works, in this paper, we prove asymptotic formulas for the k-ranks and their cumulation functions. Asymptotic inequalities between these combinatori...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2014-01, Vol.409 (2), p.729-741
Main Author: Mao, Renrong
Format: Article
Language:English
Subjects:
[formula omitted]-ranks
[formula omitted]-series
Asymptotic
Circle method
Cumulation functions
Inequalities
Partial theta functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bringmann and K. Mahlburg recently. Motivated by their works, in this paper, we prove asymptotic formulas for the k-ranks and their cumulation functions. Asymptotic inequalities between these combinatorial objects are also discovered. In particular, we show that, for fixed integer l and sufficiently large N, M(l,N)∼N(l,N) and M(l,N)
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2013.07.057