{"paper":{"title":"There are infinitely many limit points of the fractional parts of powers","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Art\\=uras Dubickas","submitted_at":"2005-12-14T10:02:19Z","abstract_excerpt":"Suppose that $\\al>1$ is an algebraic number and $\\xi>0$ is a real number. We prove that the sequence of fractional parts $\\{\\xi \\al^n\\},$ $n =1,2,3,...,$ has infinitely many limit points except when $\\al$ is a PV-number and $\\xi \\in \\Q(\\al).$ For $\\xi=1$ and $\\al$ being a rational non-integer number, this result was proved by Vijayaraghavan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512314","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"}