论文标题
泰勒的雅各比形式的扩展和theta系列之间的线性关系
Taylor expansions of Jacobi forms and linear relations among theta series
论文作者
论文摘要
我们研究了雅各比形式的晶格指数的泰勒膨胀。作为主要结果，我们将这种形式的某些空间的嵌入（无论是标量价值或矢量价值），具有任何级别的积分重量或半积极 - 具有任何特征，以任何特征，以有限多个模块化形式的空间。作为应用程序，我们研究了Jacobi Theta系列晶格指数之间的线性关系。与$ d_4 $ lattice和$ a_3 $ lattice相关的Theta系列的第二个力量之间的许多线性关系，以及与$ a_2 $ lattice相关的第三个系列功能之间的关系。我们介绍了$ d_4 $ lattice的完整Sagemath代码。
We study Taylor expansions of Jacobi forms of lattice index. As the main result, we give an embedding from certain space of such forms, whether scalar-valued or vector-valued, integral-weight or half-integral-weight, of any level, with any character, into a product of finitely many spaces of modular forms. As an application, we investigate linear relations among Jacobi theta series of lattice index. Many linear relations among the second powers of such theta series associated with the $D_4$ lattice and $A_3$ lattice are obtained, along with relations among the third powers of series associated with the $A_2$ lattice. We present the complete SageMath code for the $D_4$ lattice.
