{"paper":{"title":"Bernstein-Walsh inequalities in higher dimensions over exponential curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mark Lawrence, Shirali Kadyrov","submitted_at":"2014-12-04T14:02:19Z","abstract_excerpt":"Let ${{\\bf x}}=(x_1,\\dots,x_d) \\in [-1,1]^d$ be linearly independent over $\\mathbb Z$, set $K=\\{(e^{z},e^{x_1 z},e^{x_2 z}\\dots,e^{x_d z}): |z| \\le 1\\}.$ We prove sharp estimates for the growth of a polynomial of degree $n$, in terms of $$E_n({\\bf x}):=\\sup\\{\\|P\\|_{\\Delta^{d+1}}:P \\in \\mathcal P_n(d+1), \\|P\\|_K \\le 1\\},$$ where $\\Delta^{d+1}$ is the unit polydisk. For all ${{\\bf x}} \\in [-1,1]^d$ with linearly independent entries, we have the lower estimate $$\\log E_n({\\bf x})\\ge \\frac{n^{d+1}}{(d-1)!(d+1)} \\log n - O(n^{d+1});$$ for Diophantine $\\bf x$, we have $$\\log E_n({\\bf x})\\le \\frac{ n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1668","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"}