We prove several infinite families of $q$-series identities for false theta functions and related series. These identities are motivated by considerations of characters of modules of vertex operator superalgebras and of quantum dilogarithms. We also obtain closely related modular identities of the Gollnitz-Gordon-Andrews type. As a byproduct of our identities, we establish several identities for the Rogers dilogarithm function coming from multi $q$-hypergeometric series with "double poles".

中文翻译：

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关于假 theta 系列的 q 系列恒等式

我们证明了假 theta 函数和相关系列的几个无限系列的 $q$-系列恒等式。这些恒等式是出于对顶点算子超代数和量子二对数模的特征的考虑。我们还获得了 Gollnitz-Gordon-Andrews 类型的密切相关的模块化身份。作为恒等式的副产品，我们为来自具有“双极点”的多 $q$-超几何级数的罗杰斯二对数函数建立了几个恒等式。