{"paper":{"title":"Cusp forms for exceptional group of type $E_{7}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Henry H. Kim, Takuya Yamauchi","submitted_at":"2014-12-17T19:55:58Z","abstract_excerpt":"Let $\\bf{G}$ be the connected reductive group of type $E_{7,3}$ over $\\mathbb{Q}$ and $\\mathfrak{T}$ be the corresponding symmetric domain in $\\mathbb{C}^{27}$. Let $\\Gamma=\\bf{G}(\\mathbb{Z})$ be the arithmetic subgroup defined by Baily. In this paper, for any positive integer $k\\ge 10$, we will construct a (non-zero) holomorphic cusp form on $\\mathfrak{T}$ of weight $2k$ with respect to $\\Gamma$ from a Hecke cusp form in $S_{2k-8}(SL_2(\\mathbb{Z}))$. This lift is an analogue of Ikeda's construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5549","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"}