{"paper":{"title":"Algebraic approximations to linear combinations of powers: an extension of results by Mahler and Corvaja-Zannier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Avinash Kulkarni, Khoa D. Nguyen, Niki Myrto Mavraki","submitted_at":"2015-11-26T22:57:24Z","abstract_excerpt":"For every complex number $x$, let $\\Vert x\\Vert_{\\mathbb{Z}}:=\\min\\{|x-m|:\\ m\\in\\mathbb{Z}\\}$. Let $K$ be a number field, let $k\\in\\mathbb{N}$, and let $\\alpha_1,\\ldots,\\alpha_k$ be non-zero algebraic numbers. In this paper, we completely solve the problem of the existence of $\\theta\\in (0,1)$ such that there are infinitely many tuples $(n,q_1,\\ldots,q_k)$ satisfying $\\Vert q_1\\alpha_1^n+\\ldots+q_k\\alpha_k^n\\Vert_{\\mathbb{Z}}<\\theta^n$ where $n\\in\\mathbb{N}$ and $q_1,\\ldots,q_k\\in K^*$ having small logarithmic height compared to $n$. In the special case when $q_1,\\ldots,q_k$ have the form $q_i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08525","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"}