论文标题
划分为主要力量
Partitions into prime powers
论文作者
论文摘要
对于子集$ \ MATHCAL A \ subset \ Mathbb n $，令$ p _ {\ Mathcal a}（n）$表示限制的分区功能，该函数计数$ n $的分区，所有零件都属于$ \ Mathcal in $ a $。在本文中，我们使用Hardy-Littlewood Circle方法的变体为$ p _ {\ Mathcal a}（n）$提供渐近公式，其中$ \ Mathcal a $是$ k $ th primes的集合（固定$ k $）。这结合了沃恩（Vaughan）对素数分区的工作，并将作者先前关于划分为$ k $ th powers的结果。这个新的渐近公式是过去几年中有关限制分区功能的几个结果表明的模式的扩展。与这些结果并排比较这些结果，我们讨论了一种一般策略，通过该策略可以分析给定的$ \ Mathcal a $ $ p _ {\ Mathcal a}（n）$。
For a subset $\mathcal A\subset \mathbb N$, let $p_{\mathcal A}(n)$ denote the restricted partition function which counts partitions of $n$ with all parts lying in $\mathcal A$. In this paper, we use a variation of the Hardy-Littlewood circle method to provide an asymptotic formula for $p_{\mathcal A}(n)$, where $\mathcal A$ is the set of $k$-th powers of primes (for fixed $k$). This combines Vaughan's work on partitions into primes with the author's previous result about partitions into $k$-th powers. This new asymptotic formula is an extension of a pattern indicated by several results about restricted partition functions over the past few years. Comparing these results side-by-side, we discuss a general strategy by which one could analyze $p_{\mathcal A}(n )$ for a given set $\mathcal A$.
