{"paper":{"title":"Lattice point counting problems on step-two nilpotent Lie groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Sheng-Chen Mao","submitted_at":"2026-05-25T17:01:32Z","abstract_excerpt":"We develop the theory of lattice point counting on connected and simply connected nilpotent Lie groups of step-two, endowed with the parabolic type dilation and a family of homogeneous norms $ \\mathcal{N}_{\\alpha,M}(x, t)=\\left(|M_1x|^\\alpha + |M_2t|^{\\alpha / 2}\\right)^{1 / \\alpha}$ adapted to the dilation structure, where $\\alpha>0$ and $M_1,M_2$ are invertible matrices. With appropriate notions of lattices, the domains to be counted are balls associated to these norms, and explicit counting discrepancy estimates are deduced for all possible dimensions and all $\\alpha>0$. The bounds are shar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26033","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/2605.26033/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"}