{"paper":{"title":"On irreducible components of real exponential hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.AG","authors_text":"Cordian Riener, Nicolai Vorobjov","submitted_at":"2016-09-20T05:43:40Z","abstract_excerpt":"Fix any algebraic extension $\\mathbb K$ of the field $\\mathbb Q$ of rationals. In this article we study exponential sets $V\\subset \\mathbb R^n$. Such sets are described by the vanishing of so called exponential polynomials, i.e., polynomials with coefficients from $\\mathbb K$, in $n$ variables, and in $n$ exponential functions. The complements of all exponential sets in $\\mathbb R^n$ form a Noethrian topology on $\\mathbb R^n$, which we will call Zariski topology. Let $P \\in {\\mathbb K}[X_1, \\ldots ,X_n,U_1, \\ldots ,U_n]$ be a polynomial such that $$V=\\{ \\mathbf{x}=(x_1, \\ldots , x_n) \\in \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06025","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":""},"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"}