关于Hermitian Jacobi型的若干问题
Some aspects of Hermitian Jacobi forms
摘要：
在一次Hermitian Jacobi型空间上引入一个微分（热）算子，证明了它与Hecke算子的可换性，并利用它构造了椭圆尖点形式到Hermitian Jacobi尖点形式的提升.我们构造厄米特雅可比形式作为图像的张量积的两个副本的雅可比形式，也从微分的变量。我们确定了确定一个Hermitian Jacobi形式的傅里叶系数的个数，并利用它将Hermitian Jacobi形式的某个子空间嵌入到全模群的模形式的直和中。
英文摘要：
We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show it's commutation with certain Hecke operators and use it to construct a lift of elliptic cusp forms to Hermitian Jacobi cusp forms. We construct Hermitian Jacobi forms as the image of the tensor product of two copies of Jacobi forms and also from differentiation of the variables. We determine the number of Fourier coefficients that determine a Hermitian Jacobi form and use it to embed a certain subspace of Hermitian Jacobi forms into a direct sum of modular forms for the full modular group.
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