标题： 关于Lambert级数和迭代Eisenstein积分的 resurgence 展开 显示英文标题

标题： Resurgent expansion of Lambert series and iterated Eisenstein integrals

摘要： 我们考虑特殊的Lambert级数作为除数和的生成函数，并确定它们在单位根的有理根附近的完整转系列展开。 我们的方法还为最近在特定周期积分和弦理论散射振幅背景下引起关注的迭代艾森斯坦积分的洛朗展开和模性性质提供了新的见解。 显示英文摘要

摘要： 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.