{"paper":{"title":"Unitary monodromy implies the smoothness along the real axis for some Painlev\\'{e} VI equation, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Chang-shou Lin, Ting-Jung Kuo, Zhijie Chen","submitted_at":"2016-10-05T07:58:56Z","abstract_excerpt":"In this paper, we study the Painlev\\'{e} VI equation with parameter $(\\frac {9}{8},\\frac{-1}{8},\\frac{1}{8},\\frac{3}{8})$. We prove\n  (i) An explicit formula to count the number of poles of an algebraic solution with the monodromy group $D_{N}$, where $D_{N}$ is the dihedral group of order $2N$.\n  (ii) There are only four solutions without poles in $\\mathbb{C}\\backslash \\left \\{ 0,1\\right \\} $.\n  (iii) If the monodromy group of the associated linear ODE of a solution $\\lambda \\left( t\\right) $ is unitary, then $\\lambda ( t) $ has no poles in $\\mathbb{R}% \\backslash \\{ 0,1\\} $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01299","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"}