论文标题
模块化表格2和分区编号的应用
Hecke nilpotency for modular forms mod 2 and an application to partition numbers
论文作者
论文摘要
对Serre和Tate的一个众所周知的观察结果是，Hecke代数在$ \ Mathrm {sl} _2（\ Mathbb {Z}）$上局部对模块化形式mod 2上的作用。我们给出了一种用于计算尖端形式的Hecke Nilpotenty的程度的算法，并且我们获得了任何给定的nilpotenty的尖端形式2 mod 2的公式。使用这些结果，我们发现空间中的Hecke Nilpotency的程度没有限制分布为$ k \ rightarrow \ infty $。作为应用程序，我们使用Hecke Nilpotency研究了分区函数的均衡。
A well-known observation of Serre and Tate is that the Hecke algebra acts locally nilpotently on modular forms mod 2 on $\mathrm{SL}_2(\mathbb{Z})$. We give an algorithm for calculating the degree of Hecke nilpotency for cusp forms, and we obtain a formula for the total number of cusp forms mod 2 of any given degree of nilpotency. Using these results, we find that the degrees of Hecke nilpotency in spaces $M_k$ have no limiting distribution as $k \rightarrow \infty$. As an application, we study the parity of the partition function using Hecke nilpotency.
