论文标题
分区功能模型4
The partition function modulo 4
论文作者
论文摘要
人们普遍认为，分区函数的均衡$ p（n）$是``随机''。与这种期望相反，在本说明中，我们证明了其价值4中无限的许多一致性关系modulo 4。对于每个无正方形整数$ 1 <d \ equiv 23 \ pmod {24}，$，我们构造了一个重量2 meromormorormormorormormormormormororigic模块化表格，它是数字$ p \ big（\ frac {dm^2+1} {24} {24} {24} {24} \ big）\ pmod pmod pmod pmod 4 $ 4 $ ppmod $ p \ big（\ frac {\ frac {dm^frac {dm^frac {dm frac {frac big）的某个扭曲的生成功能。我们证明了这些系列的合适的全体形态正常化集中的无限许多线性依赖依赖性的存在。 这些结果依赖于班级数和希尔伯特类多项式的理论，以及由Bruinier和作者开发的{\ IT广义扭曲的Borcherds产品}。
It is widely believed that the parity of the partition function $p(n)$ is ``random.'' Contrary to this expectation, in this note we prove the existence of infinitely many congruence relations modulo 4 among its values. For each square-free integer $1<D\equiv 23\pmod{24},$ we construct a weight 2 meromorphic modular form that is congruent modulo 4 to a certain twisted generating function for the numbers $p\big(\frac{Dm^2+1}{24}\big)\pmod 4$. We prove the existence of infinitely many linear dependence congruences modulo 4 among suitable sets of holomorphic normalizations of these series. These results rely on the theory of class numbers and Hilbert class polynomials, and {\it generalized twisted Borcherds products} developed by Bruinier and the author.
