Resurgent expansion of Lambert series and iterated Eisenstein integrals

Dorigoni, Daniele; Kleinschmidt, Axel

doi:10.4310/cntp.2021.v15.n1.a1

Resurgent expansion of Lambert series and iterated Eisenstein integrals

Dorigoni, Daniele; Kleinschmidt, Axel

Authors

Dr Daniele Dorigoni daniele.dorigoni@durham.ac.uk
Associate Professor

Axel Kleinschmidt

Abstract

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.

Citation

Dorigoni, D., & Kleinschmidt, A. (2021). Resurgent expansion of Lambert series and iterated Eisenstein integrals. Communications in Number Theory and Physics, 15(1), 1-57. https://doi.org/10.4310/cntp.2021.v15.n1.a1

Journal Article Type	Article
Acceptance Date	Jun 5, 2020
Online Publication Date	Jan 4, 2021
Publication Date	2021
Deposit Date	Jun 29, 2021
Publicly Available Date	Oct 13, 2021
Journal	Communications in Number Theory and Physics
Print ISSN	1931-4523
Electronic ISSN	1931-4531
Publisher	International Press
Peer Reviewed	Peer Reviewed
Volume	15
Issue	1
Pages	1-57
DOI	https://doi.org/10.4310/cntp.2021.v15.n1.a1
Related Public URLs	https://arxiv.org/abs/2001.11035

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Copyright © International Press. First published in Communications in number theory and physics in 15:1 (2021), published by International Press