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The formulas are then used to study the Lu Qi-Keng problem. We produce sequences of rationals $\\gamma_j \\searrow 1$, where each $\\mathbb{H}_{\\gamma_j}$ has a Bergman kernel with zeros (while $\\mathbb{H}_1$ is known to have a zero-free kernel), resolving an open question on this domain class."},"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":"2505.20489","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2025-05-26T19:49:17Z","cross_cats_sorted":[],"title_canon_sha256":"94ef9acac36904118877e7539d167c10321540f6dfbe0cf1112b72abd8d41b99","abstract_canon_sha256":"1a32457eab8fba7c3088c20d5aeae1788db186669382aa014d19f4d5f2e9a458"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:20.417840Z","signature_b64":"V66AihfGZhsWGWttp1UHnoD2+JP41ikxXkx8toD9m37p1SuiQtxw5QuqHnAJ4MML6kjzgeBox91FLgTAKSJHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0732b12666cb17679ae89d782b58cf6e5eaeae6248a43c70d83ea2149c2b38e0","last_reissued_at":"2026-05-20T00:00:20.416972Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:20.416972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic properties and zeros of the Bergman kernel on a class of quotient domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Luke D. 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