We consider special Lambert series as generating functions of divisor sums and determine their complete transseries expansion near rational roots of unity. Our methods also yield new insights into the Laurent expansions and modularity properties of iterated Eisenstein integrals that have recently attracted attention in the context of certain period integrals and string theory scattering amplitudes.

中文翻译：

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兰伯特级数和迭代爱森斯坦积分的复苏展开

我们将特殊兰伯特级数视为除数和的生成函数，并确定它们在合一有理根附近的完整超系列展开。我们的方法还对迭代爱森斯坦积分的洛朗展开和模块化特性产生了新的见解，这些特性最近在某些周期积分和弦理论散射幅度的背景下引起了人们的注意。