{"paper":{"title":"The hexagon equations for dilogarithms and the Riemann-Hilbert problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.NT"],"primary_cat":"math.CA","authors_text":"Kimio Ueno, Shu Oi","submitted_at":"2013-01-22T08:30:17Z","abstract_excerpt":"In this article we present the hexagon equations for dilogarithms which come from the analytic continuation of the dilogarithm $\\mathrm{Li}_2(z)$ to ${\\mathbf P}^1 \\setminus {0,1,\\infty}$. The hexagon equations are equivalent to the coboundary relations for a certain 1-cocycle of holomorphic functions on ${\\mathbf P}^1$, and are solved by the Riemann-Hilbert problem of additive type. They uniquely characterize the dilogarithm under the normalization condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5105","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"}