{"paper":{"title":"Lattice point counting in Cygan--Kor\\'anyi balls on Heisenberg groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Sheng-Chen Mao, Sibei Yang","submitted_at":"2026-07-13T00:35:24Z","abstract_excerpt":"Lattice point counting in gauge balls on the Heisenberg group $\\mathbb{H}^q$ is a non-commutative analogue of the Euclidean multidimensional sphere problem, initiated by Garg, Nevo and Taylor \\cite[\\textit{Ann. Inst. Fourier}, 2015]{GNT15}. The case of particular interest is when the gauge is taken as the Cygan--Kor\\'anyi norm and the error term reads: $$\\mathcal{E}_q(t)=\\#\\left(\\mathbb{Z}^{2 q+1} \\cap \\mathcal{B}_t\\right)-\\operatorname{vol}(\\mathcal{B}_1) \\, t^{2 q+2},$$ with $\\mathcal{B}_t=\\{(v,w)\\in\\mathbb{H}^q: (|v|^4 + w^2)^{1/4} \\le t \\}$, which is closely related to the Gauss circle pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10971","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/2607.10971/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"}