{"paper":{"title":"Number systems over general orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Attila Peth\\H{o}, Jan-Hendrik Evertse, J\\\"org M. Thuswaldner, K\\'alm\\'an Gy\\H{o}ry","submitted_at":"2018-10-23T08:14:22Z","abstract_excerpt":"Let $\\mathcal{O}$ be an order, that is a commutative ring with $1$ whose additive structure is a free $\\mathbb{Z}$-module of finite rank. A generalized number system (GNS for short) over $\\mathcal{O}$ is a pair $(p,\\mathcal{D} )$ where $p\\in\\mathcal{O}[x]$ is monic with constant term $p(0)$ not a zero divisor of $\\mathcal{O}$, and where $\\mathcal{D}$ is a complete residue system modulo $p(0)$ in $\\mathcal{O}$ containing $0$. We say that $(p,\\mathcal{D})$ is a GNS over $\\mathcal{O}$ with the finiteness property if all elements of $\\mathcal{O}[x]/(p)$ have a representative in $\\mathcal{D}[x]$ (t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09710","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"}