{"paper":{"title":"Rational digit systems over finite fields and Christol's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\\"org M. Thuswaldner, Klaus Scheicher, Manuel Joseph C. Loquias, Mohamed Mkaouar","submitted_at":"2015-12-24T14:30:59Z","abstract_excerpt":"Let $P, Q\\in \\mathbb{F}_q[X]\\setminus\\{0\\}$ be two coprime polynomials over the finite field $\\mathbb{F}_q$ with $\\operatorname{deg}{P} > \\operatorname{deg}{Q}$. We represent each polynomial $w$ over $\\mathbb{F}_q$ by \\[w=\\sum_{i=0}^k\\frac{s_i}{Q}{\\left(\\frac{P}{Q}\\right)}^i\\] using a rational base $P/Q$ and digits $s_i\\in\\mathbb{F}_q[X]$ satisfying $\\operatorname{deg}{s_i} < \\operatorname{deg}{P}$. Digit expansions of this type are also defined for formal Laurent series over $\\mathbb{F}_q$. We prove uniqueness and automatic properties of these expansions. Although the $\\omega$-language of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07824","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"}