We discuss generalizations of classical theta series, requiring only some basic properties of the classical setting. As it turns out, the existence of a generalized theta transformation formula implies that the series is defined over a quasi-symmetric Siegel domain. In particular the exceptional symmetric tube domain does not admit a theta function.

中文翻译：

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管域上的 Theta 函数

我们讨论经典 theta 级数的推广，只需要经典设置的一些基本属性。事实证明，广义 theta 变换公式的存在意味着该级数是在准对称 Siegel 域上定义的。特别是特殊的对称管域不允许θ函数。