{"paper":{"title":"On Poincar\\'e series of half-integral weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Sonja \\v{Z}unar","submitted_at":"2017-11-20T12:19:43Z","abstract_excerpt":"We use Poincar\\'e series of $ K $-finite matrix coefficients of genuine integrable representations of the metaplectic cover of $ \\mathrm{SL}_2(\\mathbb R) $ to construct a spanning set for the space of cusp forms $ S_m(\\Gamma,\\chi) $, where $ \\Gamma $ is a discrete subgroup of finite covolume in the metaplectic cover of $ \\mathrm{SL}_2(\\mathbb R) $, $ \\chi $ is a character of $ \\Gamma $ of finite order, and $ m\\in\\frac52+\\mathbb Z_{\\geq0} $. We give a result on the non-vanishing of the constructed cusp forms and compute their Petersson inner product with any $ f\\in S_m(\\Gamma,\\chi) $. Using thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07281","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"}