论文标题
Hermitian Theta系列和Maaß空间在Hermitian模块化组最大离散延伸的作用下
Hermitian theta series and Maaß spaces under the action of the maximal discrete extension of the Hermitian modular group
论文作者
论文摘要
令$γ_n（\ Mathcal {\ scriptStyle {o}} _ {\ Mathbb {k}}）$表示假想的二次数字$ \ \ m athbb {k} $和$δ_{组$ su（n，n; \ mathbb {c}）$。在本文中，我们研究了Hermitian Theta系列和Maass空间的$δ_{N，\ Mathbb {K}}^*$的动作。对于$ n = 2 $，我们会找到theta lattices，以使相应的theta系列是相对于$δ_{2，\ mathbb {k}}}^*$的模块化表单，以及情况并非如此。我们的第二个重点在于研究两个不同的Maass空间。我们将看到新发现的组$δ_{2，\ Mathbb {k}}}^*$巩固了空间的不同定义。
Let $Γ_n(\mathcal{\scriptstyle{O}}_{\mathbb{K}})$ denote the Hermitian modular group of degree $n$ over an imaginary quadratic number field $\mathbb{K}$ and $Δ_{n,\mathbb{K}}^*$ its maximal discrete extension in the special unitary group $SU(n,n;\mathbb{C})$. In this paper we study the action of $Δ_{n,\mathbb{K}}^*$ on Hermitian theta series and Maass spaces. For $n=2$ we will find theta lattices such that the corresponding theta series are modular forms with respect to $Δ_{2,\mathbb{K}}^*$ as well as examples where this is not the case. Our second focus lies on studying two different Maass spaces. We will see that the new found group $Δ_{2,\mathbb{K}}^*$ consolidates the different definitions of the spaces.
