{"paper":{"title":"Spectral properties of cubic complex Pisot units","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.NT"],"primary_cat":"math.MG","authors_text":"Edita Pelantov\\'a, Tom\\'a\\v{s} Hejda","submitted_at":"2013-12-02T22:55:14Z","abstract_excerpt":"For a real number $\\beta>1$, Erd\\H{o}s, Jo\\'o and Komornik study distances between consecutive points in the set $X^m(\\beta)=\\bigl\\{\\sum_{j=0}^n a_j \\beta^j : n\\in\\mathbb N,\\,a_j\\in\\{0,1,\\dots,m\\}\\bigr\\}$. Pisot numbers play a crucial role for the properties of $X^m(\\beta)$. Following the work of Za\\\"imi, who considered $X^m(\\gamma)$ with $\\gamma\\in\\mathbb{C}\\setminus\\mathbb{R}$ and $|\\gamma|>1$, we show that for any non-real $\\gamma$ and $m < |\\gamma|^2-1$, the set $X^m(\\gamma)$ is not relatively dense in the complex plane.\n  Then we focus on complex Pisot units with a positive real conjugate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0653","kind":"arxiv","version":3},"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"}