非分明无限制分拆的一般矩定理
General moment theorems for non-distinct unrestricted partitions
摘要：
一个著名的结果从哈代和拉马努金给出了一个渐近表达式的数量可能的方式来表达一个整数的总和较小的整数。在这种情况下，我们认为一般的分区问题，写一个整数$n$作为一个总和的被加数从一个给定的序列$\gL$的非减整数。在序列$\gL$的适当假设下，我们得到的结果，使用相关的ζ函数和鞍点技术。我们还计算了序列$\gL$的高阶矩以及期望的被加数。应用程序是各种序列，包括巴恩斯和爱泼斯坦类型。这些结果在玻色-爱因斯坦凝聚的统计力学中具有潜在的意义。
英文摘要：
A well-known result from Hardy and Ramanujan gives an asymptotic expression for the number of possible ways to express an integer as the sum of smaller integers. In this vein, we consider the general partitioning problem of writing an integer $n$ as a sum of summands from a given sequence $\gL$ of non-decreasing integers. Under suitable assumptions on the sequence $\gL$, we obtain results using associated zeta-functions and saddle-point techniques. We also calculate higher moments of the sequence $\gL$ as well as the expected number of summands. Applications are made to various sequences, including those of Barnes and Epstein types. These results are of potential interest in statistical mechanics in the context of Bose-Einstein condensation.
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