论文标题
杰出组的半整合体重的模块化形式
Modular forms of half-integral weight on exceptional groups
论文作者
论文摘要
我们定义了季常典型组上半融合体重的模块化形式的概念。我们证明它们具有傅立叶系数的概念，这些概念是定义为乘法乘以$ \ pm 1 $的复数。我们分析了$ f_4 $的双重封面上的最小模块化表格$θ_{f_4} $，在loke-savin和ginzburg之后。使用$θ_{f_4} $，我们定义了一种模块化形式的权重$ \ frac {1} {2} $ on（Double Cover）$ g_2 $。我们证明，这种模块化形式的傅立叶系数在$ g_2 $上查看$ 2 $ torsion的$ 2 $ torsion in狭窄的完全真实的立方场。
We define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by $\pm 1$. We analyze the minimal modular form $Θ_{F_4}$ on the double cover of $F_4$, following Loke--Savin and Ginzburg. Using $Θ_{F_4}$, we define a modular form of weight $\frac{1}{2}$ on (the double cover of) $G_2$. We prove that the Fourier coefficients of this modular form on $G_2$ see the $2$-torsion in the narrow class groups of totally real cubic fields.
