标题： 关于分区范数的分布 显示英文标题

标题： On the distribution of the norm of partitions

摘要： 整数分划的范数被定义为其各部分的乘积。 这一统计量最近由施耐德引入，与分划ζ函数相关联。 在这篇短文中，我们利用矩方法研究了当 $n$ 在 $n \to \infty$ 的均匀概率测度下时，范数的分布情况。 我们通过奇点分析证明了矩的渐近公式，并由此表明范数在 $[0,\infty)$ 上缺乏非平凡的极限分布。 显示英文摘要

摘要： The norm of an integer partition is defined as the product of its parts. This statistic was recently introduced by Schneider in connection to partition zeta functions. In this note, we use the method of moments to study the distribution of the norm under the uniform probability measure on partitions of $n$ as $n \to \infty$. We use singularity analysis to prove asymptotics for the moments and show as a result that the norm lacks a non-trivial limiting distribution on $[0,\infty)$.