论文标题
Rademacher的猜想和扩展在产生限制分区的产品统一的根源
Rademacher's conjecture and expansions at roots of unity of products generating restricted partitions
论文作者
论文摘要
限制分区的生成函数是一个有限的产品，其每个统一根部都具有lurent膨胀。随着产品的大小增加，这些laurent系数的行为问题可以追溯到Rademacher及其在分区上的工作。在作者的Drmota，Gerhold和以前的结果的基础上，我们完成了此描述，并在每个统一根源的每个系数上都对每个系数进行了完整的渐近扩展。这些技术还显示出给Sylvester波的渐近学。
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.
