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We consider a class of Hecke characters $\\chi$, which are anticyclotomic twists of $\\phi$ with ramification in a prescribed finite set of primes. We shall prove the central vanishing order of the Hecke $L$-function $L(s,\\chi$) attached to each $\\chi$ is 0 or 1 depending on the root number $W(\\chi)$ for all but finitely many such $\\chi$."},"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":"2412.05867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-12-08T09:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"06bc7c92069bee75f1a4ebc3fd773cc385582b04de75a1a4feaa5cc6cb55ccb7","abstract_canon_sha256":"63bd797a9c3e345027feb92db6809b6fd267a0244ccc93bb0db7d0cb91c88505"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:46:10.903483Z","signature_b64":"X4d8ASK4/L8jnRyhd9DHZRymL+sr3T1lXMU+LVUA7vpcJuKntLI0ZENhfI1Kk1L+SS3Dhcr8CWUs+w22RGtiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d470b8effa378eb47a1381f813effeb06145bde18d1dad029e2a2838cc6ba200","last_reissued_at":"2026-07-05T09:46:10.902931Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:46:10.902931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $L$-functions of Hecke characters and anticyclotomic towers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Haijun Jia","submitted_at":"2024-12-08T09:15:17Z","abstract_excerpt":"In this paper, we generalize a work of Rohrlich. 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