{"paper":{"title":"Counting rational points near planar curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ayla Gafni","submitted_at":"2014-01-20T16:08:55Z","abstract_excerpt":"We find an asymptotic formula for the number of rational points near planar curves. More precisely, if $f:\\mathbb{R}\\rightarrow\\mathbb{R}$ is a sufficiently smooth function defined on the interval $[\\eta,\\xi]$, then the number of rational points with denominator no larger than $Q$ that lie within a $\\delta$-neighborhood of the graph of $f$ is shown to be asymptotically equivalent to $(\\xi-\\eta)\\delta Q^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4958","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":""},"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"}