{"paper":{"title":"An exact formula for $\\mathrm{U}(3)$ Vafa-Witten invariants on $\\mathbb{P}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.NT","authors_text":"Caner Nazaroglu, Kathrin Bringmann","submitted_at":"2018-03-25T14:58:52Z","abstract_excerpt":"Topologically twisted $\\mathcal{N} = 4$ super Yang-Mills theory has a partition function that counts Euler numbers of instanton moduli spaces. On the manifold $\\mathbb{P}^2$ and with gauge group $\\mathrm{U}(3)$ this partition function has a holomorphic anomaly which makes it a mock modular form of depth two. We employ the Circle Method to find a Rademacher expansion for the Fourier coefficients of this partition function. This is the first example of the use of Circle Method for a mock modular form of a higher depth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09270","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}