论文标题
$ O（2,1）$的普通Borcherds产品的Hecke均等
Hecke equivariance of generalized Borcherds products of type $O(2,1)$
论文作者
论文摘要
最近，证明了Borcherds的$ o（2,1）$的起重操作员的弱匡威定理，证明了$ \ g_0（n）$的$ \ g_0（n）$，并且以$ \ g_0（n）$的模块化形式的对数衍生物被明确描述了Niebur-Poincaré系列级别的复杂级别的高级级别。 In this paper, we prove that the generalized Borcherds' lifting operator of type $O(2,1)$ is Hecke equivariant under the extension of Guerzhoy's multiplicative Hecke operator on the integral weight meromorphic modular forms and the Hecke operator on half-integral weight vector-valued harmonic weak Maass forms.此外，我们表明，对数差分运算符在乘法Hecke操作员下也是Hecke Equivariant，而Hecke Operator在整体权重的Meromorphic模块化形式上也是Hecke Operatian。作为两个操作员的Hecke均衡性的应用，我们获得了扭曲的Moduli Modulo Prime Powers的扭曲痕迹的关系，并获得了扭曲的类数量Modulo Prime的关系，包括与属$ 1 $模块化曲线相关的曲线。
Recently, a weak converse theorem for Borcherds' lifting operator of type $O(2,1)$ for $\G_0(N)$ is proved and the logarithmic derivative of a modular form for $\G_0(N)$ is explicitly described in terms of the values of Niebur-Poincaré series at its divisors in the complex upper half-plane. In this paper, we prove that the generalized Borcherds' lifting operator of type $O(2,1)$ is Hecke equivariant under the extension of Guerzhoy's multiplicative Hecke operator on the integral weight meromorphic modular forms and the Hecke operator on half-integral weight vector-valued harmonic weak Maass forms. Additionally, we show that the logarithmic differential operator is also Hecke equivariant under the multiplicative Hecke operator and the Hecke operator on integral weight meromorphic modular forms. As applications of Hecke equivariance of the two operators, we obtain relations for twisted traces of singular moduli modulo prime powers and congruences for twisted class numbers modulo primes, including those associated to genus $1$ modular curves.
