几个过划分统计量的渐近性和极限分布

IF 0.7 3区 数学 Q3 MATHEMATICS
Helen W.J. Zhang, Ying Zhong
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引用次数: 0

摘要

本文主要研究过分区中几种统计量的渐近性和极限分布。作为初步结果,我们利用渐近方法证明了过分割中不同部分和不同整数的数目是渐近正态的,推广了Corteel和Hitczenko的结果。此外,我们研究了两类由Bringmann和Lovejoy最初引入的过分区曲柄统计量的渐近性和分布性。利用Hardy-Ramanujan圆方法,我们导出了这两个曲柄的矩的渐近公式,以及Jennings-Shaffer提出的对称矩的渐近公式。在此基础上,我们采用矩的概率方法来证明两个曲柄在适当归一化时渐近地遵循逻辑分布。因此,我们的结果恢复了Zapata Rolon首先用Wright圆法得到的正矩的渐近公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotics and limiting distributions of several overpartition statistics
This paper primarily is dedicated to studying the asymptotics and limiting distributions of several statistics in overpartitions. As a preliminary result, we use asymptotic methods to prove that the number of distinct parts and distinct integers in overpartitions is asymptotically normal, extending the results of Corteel and Hitczenko. Furthermore, we investigate the asymptotic and distributional properties of two types of crank statistics for overpartitions, originally introduced by Bringmann and Lovejoy. Utilizing the Hardy-Ramanujan circle method, we derive asymptotic formulas for the moments of these two cranks, as well as for the symmetrized moments proposed by Jennings-Shaffer. Building on these, we employ the probabilistic method of moments to prove that both two cranks asymptotically follow a logistic distribution when appropriately normalized. Consequently, our results recover the asymptotic formulas for the positive moments first obtained by Zapata Rolon using Wright's circle method.
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来源期刊
Journal of Number Theory
Journal of Number Theory 数学-数学
CiteScore
1.30
自引率
14.30%
发文量
122
审稿时长
16 weeks
期刊介绍: The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.
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