Resurgent Lambert series with characters

Fuente: arXiv
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Auteurs principaux: Broadhurst, David, Dorigoni, Daniele
Format: Preprint
Publié: 2025
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author Broadhurst, David
Dorigoni, Daniele
author_facet Broadhurst, David
Dorigoni, Daniele
contents We consider certain Lambert series as generating functions of divisor sums twisted by Dirichlet characters and compute their exact resurgent transseries expansion near $q=1^-$. For special values of the parameters, these Lambert series are expressible in terms of iterated integrals of holomorphic Eisenstein series twisted by the same characters and the transseries representation is a direct consequence of the action of Fricke involution on such twisted Eisenstein series. When the parameters of the Lambert series are generic the transseries representation provides for a quantum-modular version of Fricke involution which for a particular example we show being equivalent to modular resurgent structures found in topological strings observables.
format Preprint
id arxiv_https___arxiv_org_abs_2507_21352
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Resurgent Lambert series with characters
Broadhurst, David
Dorigoni, Daniele
Number Theory
High Energy Physics - Theory
We consider certain Lambert series as generating functions of divisor sums twisted by Dirichlet characters and compute their exact resurgent transseries expansion near $q=1^-$. For special values of the parameters, these Lambert series are expressible in terms of iterated integrals of holomorphic Eisenstein series twisted by the same characters and the transseries representation is a direct consequence of the action of Fricke involution on such twisted Eisenstein series. When the parameters of the Lambert series are generic the transseries representation provides for a quantum-modular version of Fricke involution which for a particular example we show being equivalent to modular resurgent structures found in topological strings observables.
title Resurgent Lambert series with characters
topic Number Theory
High Energy Physics - Theory
url https://arxiv.org/abs/2507.21352