{"paper":{"title":"Vector-valued automorphic forms and vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CA"],"primary_cat":"math.NT","authors_text":"Abdellah Sebbar, Hicham Saber","submitted_at":"2013-12-10T23:04:42Z","abstract_excerpt":"While vector-valued automorphic forms can be defined for an arbitrary Fuchsian group $\\Gamma$ and an arbitrary representation $R$ of $\\Gamma$ in GL$(n,{\\mathbb C})$, their existence has been established in the literature only when restrictions are imposed on both $\\Gamma$ and $R$. In this paper, we prove the existence of $n$ linearly independent vector-valued automorphic forms for any Fuchsian group $\\Gamma$ and any $n$-dimensional complex representation $R$ of $\\Gamma$. To this end, we realize these automorphic forms as global sections of a special rank $n$ vector bundle built using solutions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2992","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"}