The generating function for restricted partitions is a finite product with a Laurent expansion at each root of unity. The question of the behavior of these Laurent coefficients as the size of the product increases goes back to Rademacher and his work on partitions. Building on the methods of Drmota, Gerhold and previous results of the author, we complete this description and give the full asymptotic expansion of each coefficient at every root of unity. These techniques are also shown to give the asymptotics of Sylvester waves.

中文翻译：

---

Rademacher 猜想和生成受限分区的乘积统一根的扩展

受限分区的生成函数是一个有限乘积，在每个单位根都有一个 Laurent 展开。随着乘积大小的增加，这些 Laurent 系数的行为问题可以追溯到 Rademacher 和他在分区方面的工作。基于 Drmota、Gerhold 的方法和作者之前的结果，我们完成了这个描述，并在每个单位根处给出了每个系数的完全渐近展开。这些技术还显示出西尔维斯特波的渐近线。