一个多重奇点的Meinardus定理
A Meinardus theorem with multiple singularities
摘要：
Meinardus证明了当权的Dirichlet生成函数在正实轴上有一个极点时，关于权分划数的渐近性的一般定理。继续\cite{GSE}，我们推导出三种基本类型的可分解的组合结构（或，等价地，在统计力学中的理想气体模型）的大小$n$，当他们的Dirichlet生成函数在正实轴上有多个单极点的数量的渐近。我们的定理适用的例子包括与矢量划分和量子场论有关的例子。我们的加权分区数的渐近公式反驳了物理文献中所接受的信念，即渐近中的主项是由最右边的极点决定的。
英文摘要：
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.
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