{"paper":{"title":"Galois groups for integrable and projectively integrable linear difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.RT"],"primary_cat":"math.AC","authors_text":"Carlos E. Arreche, Michael F. Singer","submitted_at":"2016-07-29T20:09:59Z","abstract_excerpt":"We consider first-order linear difference systems over $\\mathbb{C}(x)$, with respect to a difference operator $\\sigma$ that is either a shift $\\sigma:x\\mapsto x+1$, $q$-dilation $\\sigma:x\\mapsto qx$ with $q\\in{\\mathbb{C}^\\times}$ not a root of unity, or Mahler operator $\\sigma:x\\mapsto x^q$ with $q\\in\\mathbb{Z}_{\\geq 2}$. Such a system is integrable if its solutions also satisfy a linear differential system; it is projectively integrable if it becomes integrable \"after moding out by scalars.\" We apply recent results of Sch\\\"{a}fke and Singer to characterize which groups can occur as Galois gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00015","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"}