{"paper":{"title":"Existence of meromorphic solutions of first order difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Risto Korhonen, Yueyang Zhang","submitted_at":"2017-08-25T08:32:28Z","abstract_excerpt":"It is shown that if It is shown that if\n  \\begin{equation}\\label{abstract_eq}\n  f(z+1)^n=R(z,f),\\tag{\\dag}\n  \\end{equation} where $R(z,f)$ is rational in $f$ with meromorphic coefficients and $\\deg_f(R(z,f))=n$, has an admissible meromorphic solution, then either $f$ satisfies a difference linear or Riccati equation with meromorphic coefficients, or \\eqref{abstract_eq} can be transformed into one in a list of ten equations with certain meromorphic or algebroid coefficients. In particular, if \\eqref{abstract_eq}, where the assumption $\\deg_f(R(z,f))=n$ has been discarded, has rational coefficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07647","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"}