{"paper":{"title":"New Subexponential Fewnomial Hypersurface Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AG","authors_text":"Jens Forsg{\\aa}rd, J. Maurice Rojas, Mounir Nisse","submitted_at":"2017-10-02T04:44:52Z","abstract_excerpt":"Suppose $c_1,\\ldots,c_{n+k}$ are real numbers, $\\{a_1,\\ldots,a_{n+k}\\}\\!\\subset\\!\\mathbb{R}^n$ is a set of points not all lying in the same affine hyperplane, $y\\!\\in\\!\\mathbb{R}^n$, $a_j\\cdot y$ denotes the standard real inner product of $a_j$ and $y$, and we set $g(y)\\!:=\\!\\sum^{n+k}_{j=1} c_j e^{a_j\\cdot y}$. We prove that, for generic $c_j$, the number of connected components of the real zero set of $g$ is $O\\!\\left(n^2+\\sqrt{2}^{k^2}(n+2)^{k-2}\\right)$. The best previous upper bounds, when restricted to the special case $k\\!=\\!3$ and counting just the non-compact components, were already "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00481","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"}