{"paper":{"title":"Convolution identities for divisor sums and modular forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Danylo Radchenko, Kim Klinger-Logan, Ksenia Fedosova","submitted_at":"2023-12-01T16:58:30Z","abstract_excerpt":"We prove exact identities for convolution sums of divisor functions of the form $\\sum_{n_1 \\in \\mathbb{Z} \\smallsetminus \\{0,n\\}}\\varphi(n_1,n-n_1)\\sigma_{2m_1}(n_1)\\sigma_{2m_2}(n-n_1)$ where $\\varphi(n_1,n_2)$ is a Laurent polynomial with logarithms for which the sum is absolutely convergent. Such identities are motivated by computations in string theory and prove and generalize a conjecture of Chester, Green, Pufu, Wang, and Wen from \\cite{CGPWW}. Originally, it was suspected that such sums, suitably extended to $n_1\\in\\{0,n\\}$ should vanish, but in this paper we find that in general they g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.00722","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/2312.00722/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"}