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We prove the following effective non-vanishing result: At least $50 \\%$ of the central values $L_j(1/2)$ with $\\kappa_j \\leq T$ do not vanish as $T\\rightarrow \\infty$. Furthermore, we establish effective non-vanishing results in short intervals."},"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":"1810.07991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-18T11:23:35Z","cross_cats_sorted":[],"title_canon_sha256":"ad682ffa65538ce4814917de282c6a4094ce0cc7ac29474a75d2dd972a5c4f37","abstract_canon_sha256":"b99c913b426f17a43e2d025fe9664d5cdd82f228af0e4debfbe4fa1abe0fadd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:30.326736Z","signature_b64":"LEXVRJNcwtVthyIANnW5v1McWK7fjaIZCPO8nrIswxz9WQLHYJsGXTN/t6rN7pap8MXIT+qVl0uHKUROfGvRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6166f30c1928d47780738313473afe118c7fcbaf9873c624d4dbaabcda46e3f7","last_reissued_at":"2026-05-17T23:58:30.326119Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:30.326119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-vanishing of Maass form L-functions at the critical point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anders S\\\"odergren, Bingrong Huang, Olga Balkanova","submitted_at":"2018-10-18T11:23:35Z","abstract_excerpt":"In this paper, we consider the family $\\{L_j(s)\\}_{j=1}^{\\infty}$ of $L$-functions associated to an orthonormal basis $\\{u_j\\}_{j=1}^{\\infty}$ of even Hecke-Maass forms for the modular group $SL(2, Z)$ with eigenvalues $\\{\\lambda_j=\\kappa_{j}^{2}+1/4\\}_{j=1}^{\\infty}$. We prove the following effective non-vanishing result: At least $50 \\%$ of the central values $L_j(1/2)$ with $\\kappa_j \\leq T$ do not vanish as $T\\rightarrow \\infty$. 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