{"paper":{"title":"Mirror symmetry, mixed motives and $\\zeta(3)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.NT"],"primary_cat":"math.AG","authors_text":"Minhyong Kim, Wenzhe Yang","submitted_at":"2017-10-06T10:49:23Z","abstract_excerpt":"In this paper, we present an application of mirror symmetry to arithmetic geometry. The main result is the computation of the period of a mixed Hodge structure, which lends evidence to its expected motivic origin. More precisely, given a mirror pair $(M,W)$ of Calabi-Yau threefolds, the prepotential of the complexified Kahler moduli space of $M$ admits an expansion with a constant term that is frequently of the form $$-3\\, \\chi (M) \\,\\zeta(3)/(2 \\pi i)^3+r,$$ where $r \\in \\mathbb{Q}$ and $\\chi(M)$ is the Euler characteristic of $M$. We focus on the mirror pairs for which the deformation space "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02344","kind":"arxiv","version":3},"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"}