Resurgent expansion of Lambert series and iterated Eisenstein integrals

Dorigoni, Daniele; Kleinschmidt, Axel

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