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We show that the number of class group characters $\\chi$ with bounded ramification such that $L'(1, A, \\chi) \\neq 0$ increases with the absolute value of the discriminant of $K$.\n  We also consider a rather general rank zero situation. Let $\\pi$ be a cuspidal cohomological automorphic representation over $\\GL_{2}(\\BA_{F})"},"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":"1712.01465","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-05T03:36:42Z","cross_cats_sorted":[],"title_canon_sha256":"53f53ea324b38c61ed7bff42159a1c3585309ac82f0094b5b3ef2eadabce5687","abstract_canon_sha256":"7429305e5d9dd714f783a1fcd2325e410d1b7f0940e1c6d50c519347648f3c93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:23:19.628648Z","signature_b64":"L7PWBmaGNKiFETyAQugZe4D+jsutlvFFeDJioO2fIAicdiYGw1DGOVPsFmimTzvKttH5PP1yC6Qw4TJd7ZImAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b093f7e21a9b4964e0e4d032c07a8c3b7a6227d2366a7caceeea78ffe51148e0","last_reissued_at":"2026-07-05T00:23:19.628089Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:23:19.628089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Horizontal non-vanishing of Heegner points and toric periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ashay A. Burungale, Ye Tian","submitted_at":"2017-12-05T03:36:42Z","abstract_excerpt":"Let $F/\\mathbb{Q}$ be a totally real field and $A$ a modular $\\GL_2$-type abelian variety over $F$. Let $K/F$ be a CM quadratic extension. Let $\\chi$ be a class group character over $K$ such that the Rankin-Selberg convolution $L(s,A,\\chi)$ is self-dual with root number $-1$. We show that the number of class group characters $\\chi$ with bounded ramification such that $L'(1, A, \\chi) \\neq 0$ increases with the absolute value of the discriminant of $K$.\n  We also consider a rather general rank zero situation. 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