{"paper":{"title":"Holomorphic projection for $\\mathop{Sp}_2(\\mathbb R)$ -- the case of weight $(4,4)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kathrin Maurischat","submitted_at":"2016-02-26T08:12:01Z","abstract_excerpt":"We define non-holomorphic Poincar\\'e series of exponential type for symplectic groups $\\mathop{Sp}_m(\\mathbb R)$ and continue them analytically in case $m=2$ for the small weight $(4,4)$. For this we construct certain Casimir operators and study the spectral properties of their resolvents on $L^2(\\Gamma\\backslash \\mathop{Sp}_2(\\mathbb R))$. Using the holomorphically continued Poincar\\'e series, the holomorphic projection is described in terms of Fourier coefficients using Sturm's operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08231","kind":"arxiv","version":1},"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"}