We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to the second author.

中文翻译：

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双半平面上的模块化形式

我们在双半平面上为半整数权重制定了模形式的概念，并解释了它与通常的模形式概念的关系。由于第二作者，我们提供的结构与某些物理考虑兼容。