{"paper":{"title":"Number systems over orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Attila Peth\\H{o}, J\\\"org Thuswaldner","submitted_at":"2017-08-16T08:21:33Z","abstract_excerpt":"Let $\\mathbb{K}$ be a number field of degree $k$ and let $\\mathcal{O}$ be an order in $\\mathbb{K}$. A \\emph{generalized number system over $\\mathcal{O}$} (GNS for short) is a pair $(p,\\mathcal{D})$ where $p \\in \\mathcal{O}[x]$ is monic and $\\mathcal{D}\\subset\\mathcal{O}$ is a complete residue system modulo $p(0)$ containing $0$. If each $a \\in \\mathcal{O}[x]$ admits a representation of the form $a \\equiv \\sum_{j =0}^{\\ell-1} d_j x^j \\pmod{p}$ with $\\ell\\in\\mathbb{N}$ and $d_0,\\ldots, d_{\\ell-1}\\in\\mathcal{D}$ then the GNS $(p,\\mathcal{D})$ is said to have the \\emph{finiteness property}. To a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04800","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"}