定义在随机排列上的强加法函数的方差

IF 0.5 4区数学 Q3 MATHEMATICS

Lithuanian Mathematical Journal Pub Date : 2024-06-24 DOI:10.1007/s10986-024-09637-z

Arvydas Karbonskis, Eugenijus Manstavičius

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引用次数: 0

摘要

在过去几十年里，Turán-Kubilius 不等式在加法数论函数中的应用逐渐普及，受此启发，我们研究了定义在从对称组中均匀抽取的随机排列上的加法函数的方差。我们扩展了克里马维奇乌斯（Klimavičius）和曼斯塔维奇乌斯（Manstavičius）2018 年针对完全加法函数情况所做的最优估计，并在函数为强加法函数时得到了渐近尖锐的上界和下界。上界估计类似于库比留斯 1985 年在数论中建立的估计。

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Variance of a strongly additive function defined on random permutations

Inspired by unfading popularity of the Turán–Kubilius inequality for additive number theoretic functions within the last decades, we examine the variance of additive functions defined on random permutations uniformly taken from the symmetric group. Extending the optimal estimate achieved in 2018 by Klimavičius and Manstavičius for the case of completely additive functions, we obtain asymptotically sharp upper and lower bounds when the functions are strongly additive. The upper estimates are analogous to that established in number theory by Kubilius in 1985.

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来源期刊

Lithuanian Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Lithuanian Mathematical Journal publishes high-quality original papers mainly in pure mathematics. This multidisciplinary quarterly provides mathematicians and researchers in other areas of science with a peer-reviewed forum for the exchange of vital ideas in the field of mathematics. The scope of the journal includes but is not limited to: Probability theory and statistics; Differential equations (theory and numerical methods); Number theory; Financial and actuarial mathematics, econometrics.