论文标题
伯格曼空间零集，模块化形式，冯·诺伊曼代数和有序组
Bergman space zero sets, modular forms, von Neumann algebras and ordered groups
论文作者
论文摘要
$ a^2_α$将表示加权$ l^2 $ bergman空间。给定开放单元光盘的子集$ s $我们定义$ω$，为$ \ {s | \存在于a^2_ {s-2}中的f \ f \ neq 0，\ mbox {具有$ s $作为零set} \} $。通过hardy Space上的经典结果，可以在hardy Space上进行$ s $，其中$ω（s）= 1 $。使用von Neumann尺寸技术和尖端表格，我们提供了$ s $的示例，其中$ 1 <ω（s）<\ infty $。通过在某些Fuchsian组上使用左订单，如果$ω$是Fuchsian组的轨道，我们可以准确地计算$ω$。这项技术还使我们能够以新的方式得出尖端形式的零的知名结果，并确实计算了\ pslz模块化形式的整个代数。
$A^2_α$ will denote the weighted $L^2$ Bergman space. Given a subset $S$ of the open unit disc we define $Ω(S)$ to be the infimum of $\{s| \exists f \in A^2_{s-2}, f\neq 0, \mbox{ having $S$ as its zero set} \}$.By classical results on Hardy space there are sets $S$ for which $Ω(S)=1$. Using von Neumann dimension techniques and cusp forms we give examples of $S$ where $1<Ω(S)<\infty$. By using a left order on certain Fuchsian groups we are able to calculate $Ω(S)$ exactly if $Ω(S)$ is the orbit of a Fuchsian group. This technique also allows us to derive in a new way well known results on zeros of cusp forms and indeed calculate the whole algebra of modular forms for \pslz.
