{"paper":{"title":"On distribution of points with algebraically conjugate coordinates in neighborhood of smooth curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anna Gusakova, Friedrich G\\\"otze, Vasili Bernik","submitted_at":"2016-08-02T15:45:55Z","abstract_excerpt":"Let $\\varphi:\\mathbb{R}\\rightarrow \\mathbb{R}$ be a continuously differentiable function on an interval $J\\subset\\mathbb{R}$ and let $\\boldsymbol{\\alpha}=(\\alpha_1,\\alpha_2)$ be a point with algebraically conjugate coordinates such that the minimal polynomial $P$ of $\\alpha_1,\\alpha_2$ is of degree $\\leq n$ and height $\\leq Q$. Denote by $M^n_\\varphi(Q,\\gamma, J)$ the set of such points $\\boldsymbol{\\alpha}$ such that $|\\varphi(\\alpha_1)-\\alpha_2|\\leq c_1 Q^{-\\gamma}$. We show that for a real $0<\\gamma<1$ and any sufficiently large $Q$ there exist positive values $c_2<c_3$, where $c_i=c_i(n)$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00873","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"}