{"paper":{"title":"Counting Rational Points In Non-Isotropic Neighborhoods of Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Rajula Srivastava","submitted_at":"2024-07-03T12:52:33Z","abstract_excerpt":"In this manuscript, we initiate the study of the number of rational points with bounded denominators, contained in a non-isotropic $\\delta_1\\times\\ldots\\times \\delta_R$ neighborhood of a compact submanifold $\\mathcal{M}$ of codimension $R$ in $\\mathbb{R}^{M}$. We establish an upper bound for this counting function which holds when $\\mathcal{M}$ satisfies a strong curvature condition, first introduced by Schindler-Yamagishi in \\cite{schindler2022density}. Further, even in the isotropic case when $\\delta_1=\\ldots=\\delta_R=\\delta$, we obtain an asymptotic formula which holds beyond the range of d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03078","kind":"arxiv","version":3},"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/2407.03078/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"}