{"paper":{"title":"How far can you see in a forest?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Faustin Adiceam","submitted_at":"2015-09-14T16:37:39Z","abstract_excerpt":"We address a visibility problem posed by Solomon & Weiss. More precisely, in any dimension $n := d + 1 \\ge 2$, we construct a forest $\\F$ with finite density satisfying the following condition : if $\\e > 0$ denotes the radius common to all the trees in $\\F$, then the visibility $\\V$ therein satisfies the estimate $\\V(\\e) = O(\\e^{-2d-\\eta})$ for any $\\eta > 0$, no matter where we stand and what direction we look in. The proof involves Fourier analysis and sharp estimates of exponential sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04188","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"}