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Resurgent expansion of Lambert series and iterated Eisenstein integrals
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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.
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Cited by 2 Pith papers
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Resurgent Lambert series with characters
A complete transseries expansion is derived for doubly Dirichlet-twisted Lambert series near q=1, with applications to quantum modularity and topological string spectral traces.
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Resurgent Lambert series from Feynman and beyond
Sunrise/banana Feynman integrals and topological-string spectral traces are Lambert series twisted by Dirichlet characters; the P^{m,n} case with conductor N=m+n+1 splits into terminating even-character contributions ...
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