Resurgent Lambert series with characters
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911081521217536 |
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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 |