{"paper":{"title":"Description of spectra of quadratic Pisot units","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Edita Pelantov\\'a, Kate\\v{r}ina Pastir\\v{c}\\'akov\\'a, Zuzana Mas\\'akov\\'a","submitted_at":"2014-02-07T10:04:27Z","abstract_excerpt":"The spectrum of a real number $\\beta>1$ is the set $X^{m}(\\beta)$ of $p(\\beta)$ where $p$ ranges over all polynomials with coefficients restricted to ${\\mathcal A}=\\{0,1,\\dots,m\\}$. For a quadratic Pisot unit $\\beta$, we determine the values of all distances between consecutive points and their corresponding frequencies, by recasting the spectra in the frame of the cut-and-project scheme. We also show that shifting the set ${\\mathcal A}$ of digits so that it contains at least one negative element, or considering negative base $-\\beta$ instead of $\\beta$, the gap sequence of the generalized spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1582","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"}