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If $r$ is odd, $n\\le r <2n$, then under a natural hypothesis on the theta representations, we show that $\\Theta_{2n}^{(r)}$ may be used to construct a generic representation $\\sigma_{2n-r+1}^{(2r)}$ on the $2r$-fold cover of $Sp_{2n-r+1}$. Moreover, when $r=n$ the Whittaker functions of this representation attached to factorizable data are factorizable, and the unramified local factors ma"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.04970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T16:09:04Z","cross_cats_sorted":[],"title_canon_sha256":"085883f59238d423b263bed65e7ada8f85a2a00bedbb6443366753298b7e993c","abstract_canon_sha256":"8255a10dd2b23200462b9860508670188163e715d01201ca1c3c8f40a2b22420"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:34.755408Z","signature_b64":"JAAWn4Ozuwq4IARlhv/G0pvyoWb67JYe6aUZuxswpbT04Wa/tiozpE3HSj/y3F9rXfLehAjRHxZuGAbUG+2OCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b0ea912a5253da15d74e9e31643f123cf82020428ef45d2b42aeb905d58df11","last_reissued_at":"2026-05-17T23:48:34.754677Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:34.754677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theta Functions on Covers of Symplectic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Ginzburg, Solomon Friedberg","submitted_at":"2016-01-19T16:09:04Z","abstract_excerpt":"We study the automorphic theta representation $\\Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$. 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