论文标题
带有CM和应用的Jacobi形式
Jacobi forms with CM and applications
论文作者
论文摘要
我们定义具有复杂乘法的雅各比形式。它们类似于具有复杂乘法的模块化形式，它们是由相关假想二次场的Hecke字符构造的。从这种结构中，我们获得了一种雅各比形式，该形式专门针对$η（τ）^{26} $，以突出戴森和塞雷的开放问题。我们提供了具有复杂乘法的雅各比形式的其他示例和应用，包括构建与椭圆曲线相关的theta块，并具有复杂的乘法以及一致的新家族和曲柄的某些分区功能。
We define Jacobi forms with complex multiplication. Analogous to modular forms with complex multiplication, they are constructed from Hecke characters of the associated imaginary quadratic field. From this construction we obtain a Jacobi form which specializes to $η(τ)^{26}$ which we present to highlight an open question of Dyson and Serre. We give other examples and applications of Jacobi forms with complex multiplication including constructing theta blocks associated to elliptic curves with complex multiplication and new families of congruences and cranks for certain partition functions.
