{"paper":{"title":"Counting lattice points and o-minimal structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO","math.MG"],"primary_cat":"math.NT","authors_text":"Fabrizio Barroero, Martin Widmer","submitted_at":"2012-10-22T16:00:10Z","abstract_excerpt":"Let $\\Lambda$ be a lattice in $\\R^n$, and let $Z\\subseteq \\R^{m+n}$ be a definable family in an o-minimal structure over $\\R$. We give sharp estimates for the number of lattice points in the fibers $Z_T={x\\in \\R^n: (T,x)\\in Z}$. Along the way we show that for any subspace $\\Sigma\\subseteq\\R^n$ of dimension $j>0$ the $j$-volume of the orthogonal projection of $Z_T$ to $\\Sigma$ is, up to a constant depending only on the family $Z$, bounded by the maximal $j$-dimensional volume of the orthogonal projections to the $j$-dimensional coordinate subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5943","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"}