{"paper":{"title":"Algebraic sums and products of univoque bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DS","authors_text":"Derong Kong, Karma Dajani, Vilmos Komornik, Wenxia Li","submitted_at":"2017-10-09T20:02:21Z","abstract_excerpt":"Given $x\\in(0, 1]$, let $\\mathcal U(x)$ be the set of bases $q\\in(1,2]$ for which there exists a unique sequence $(d_i)$ of zeros and ones such that $x=\\sum_{i=1}^\\infty d_i/q^i$. L\\\"{u}, Tan and Wu (2014) proved that $\\mathcal U(x)$ is a Lebesgue null set of full Hausdorff dimension. In this paper, we show that the algebraic sum $\\mathcal U(x)+\\lambda\\mathcal U(x)$ and product $\\mathcal U(x)\\cdot\\mathcal U(x)^\\lambda$ contain an interval for all $x\\in(0, 1]$ and $\\lambda\\ne 0$. As an application we show that the same phenomenon occurs for the set of non-matching parameters studied by the firs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03291","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"}