{"paper":{"title":"Resurgent Lambert series from Feynman and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Daniele Dorigoni, David Broadhurst","submitted_at":"2026-07-15T16:52:52Z","abstract_excerpt":"Lambert series of the form $\\sum_{n>0}a(n)q^n/(1-q^n)$ are ubiquitous in mathematical physics. In particular, 2-loop sunrise and 3-loop banana Feynman diagrams yield Lambert series with $a(n)$ of the form $\\chi(n)/n^s$ where $\\chi(n)$ is a Dirichlet character. Resurgence concerns the singular limit as $|q|$ approaches 1. In the Feynman cases we can control this limit, obtaining rapidly convergent expressions, since the Lambert series are iterated integrals of holomorphic Eisenstein series twisted by a character. We generalize this result, to include modular resurgent structures found in topolo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14020","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14020/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}