{"paper":{"title":"Endoscopic lifts to the Siegel modular threefold related to Klein's cubic threefold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Takeo Okazaki, Takuya Yamauchi","submitted_at":"2010-08-12T06:24:32Z","abstract_excerpt":"Let $A^{lev}_{11}$ be the moduli space of (1,11)-polarized abelian surfaces with level structure of canonical type. Let $\\chi$ be a finite character of order 5 with conductor 11. In this paper we construct five endoscopic lifts $\\Pi_i,0\\le i\\le 4$ from two elliptic modular forms $f\\otimes\\chi^i$ of weight 2 and $g\\otimes\\chi^i$ of weight 4 with complex multiplication by $Q(\\sqrt{-11})$ such that ${\\Pi_i}_\\infty$ gives a non-holomorphic differential form on $A^{lev}_{11}$ for each $i$. Then the spinor L-function is of form $L(f\\otimes\\chi^i,s-1)L(g\\otimes\\chi^i,s)$ such that $L(g\\otimes\\chi^i,s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2052","kind":"arxiv","version":7},"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"}