{"paper":{"title":"Meromorphic solutions of algebraic difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Katsuya Ishizaki, Risto Korhonen","submitted_at":"2017-01-05T08:03:01Z","abstract_excerpt":"It is shown that the difference equation \\begin{equation}\\label{abseq} (\\Delta f(z))^2=A(z)(f(z)f(z+1)-B(z)), \\qquad\\qquad (1) \\end{equation} where $A(z)$ and $B(z)$ are meromorphic functions, possesses a continuous limit to the differential equation \\begin{equation}\\label{abseq2} (w')^2=A(z)(w^2-1),\\qquad\\qquad (2) \\end{equation} which extends to solutions in certain cases. In addition, if (1) possesses two distinct transcendental meromorphic solutions, it is shown that these solutions satisfy an algebraic relation, and that their growth behaviors are almost same in the sense of Nevanlinna un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01235","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"}