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Resurgent expansion of Lambert series and iterated Eisenstein integrals

Dorigoni, Daniele and Kleinschmidt, Axel (2021) 'Resurgent expansion of Lambert series and iterated Eisenstein integrals.', Communications in number theory and physics., 15 (1). pp. 1-57.


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.

Item Type:Article
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Publisher statement:Copyright © International Press. First published in Communications in number theory and physics in 15:1 (2021), published by International Press
Date accepted:05 June 2020
Date deposited:13 October 2021
Date of first online publication:04 January 2021
Date first made open access:13 October 2021

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