整数、多项式和置换分解的狄利克雷定律

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-09-06 DOI:10.1017/S0305004123000427

Sun-Kai Leung

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引用次数: 1

摘要

设$k \geqslant 2$为整数。我们通过多维轮廓积分证明了整数分解成k个部分遵循Dirichlet分布$\mathrm{Dir}\left({1}/{k},\ldots,{1}/{k}\right)$，从而推广了在$k=2$。这同样适用于多项式或排列的因式分解。具有任意参数的狄利克雷分布可以类似地建模。

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Dirichlet law for factorisation of integers, polynomials and permutations

Abstract Let $k \geqslant 2$ be an integer. We prove that factorisation of integers into k parts follows the Dirichlet distribution $\mathrm{Dir}\left({1}/{k},\ldots,{1}/{k}\right)$ by multidimensional contour integration, thereby generalising the Deshouillers–Dress–Tenenbaum (DDT) arcsine law on divisors where $k=2$ . The same holds for factorisation of polynomials or permutations. Dirichlet distribution with arbitrary parameters can be modelled similarly.

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.