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Each $f\\in\\mathcal{V}_p(\\lambda)$ has the following Taylor expansion:\n  $$\n  f(z)=z+\\sum_{n=2}^{\\infty}a_n(f) z^n, \\quad |z|<p.\n  $$\n  In \\cite{BF-3}, we conjectured that\n  $$\n  |a_n(f)|\\leq \\frac{1-(\\lambda p^2)^n}{p^{n-1}(1-\\lambda p^2)}\\quad \\mbox{for}\\quad n\\geq3. $$ In the present a"},"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":"1712.02958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-12-08T06:35:32Z","cross_cats_sorted":[],"title_canon_sha256":"1cad0bb6658348c02fcc08374f38b03a712cbf24dca7593e30f3bf5c29fbb9fc","abstract_canon_sha256":"9787e04fc46bf392a4c6a26f6b3999cd7bd4fc72178cb703ab61215ac0051adf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:28.789191Z","signature_b64":"iz0l+5stfNgC5piEmCwBqlTfu/uKy9We9pBoiDl2AL5cISjvI8C3sh5DTN45mv0ml4shAZZQte8pdg0M0qeXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48c75009619344a7448147fc62231fc67e0c036e8cc9abe31924f27a934fa681","last_reissued_at":"2026-05-18T00:28:28.788687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:28.788687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Taylor coefficients of a subclass of meromorphic univalent functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Firdoshi Parveen","submitted_at":"2017-12-08T06:35:32Z","abstract_excerpt":"Let $\\mathcal{V}_p(\\lambda)$ be the collection of all functions $f$ defined in the unit disc $\\ID$ having a simple pole at $z=p$ where $0<p<1$ and analytic in $\\ID\\setminus\\{p\\}$ with $f(0)=0=f'(0)-1$ and satisfying the differential inequality $|(z/f(z))^2 f'(z)-1|< \\lambda $ for $z\\in \\ID$, $0<\\lambda\\leq 1$. Each $f\\in\\mathcal{V}_p(\\lambda)$ has the following Taylor expansion:\n  $$\n  f(z)=z+\\sum_{n=2}^{\\infty}a_n(f) z^n, \\quad |z|<p.\n  $$\n  In \\cite{BF-3}, we conjectured that\n  $$\n  |a_n(f)|\\leq \\frac{1-(\\lambda p^2)^n}{p^{n-1}(1-\\lambda p^2)}\\quad \\mbox{for}\\quad n\\geq3. $$ In the present a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02958","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.02958","created_at":"2026-05-18T00:28:28.788762+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.02958v1","created_at":"2026-05-18T00:28:28.788762+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02958","created_at":"2026-05-18T00:28:28.788762+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDDVACLBSNCK","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDDVACLBSNCKOREB","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDDVACLB","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ","json":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ.json","graph_json":"https://pith.science/api/pith-number/JDDVACLBSNCKOREBI76GEIY7YZ/graph.json","events_json":"https://pith.science/api/pith-number/JDDVACLBSNCKOREBI76GEIY7YZ/events.json","paper":"https://pith.science/paper/JDDVACLB"},"agent_actions":{"view_html":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ","download_json":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ.json","view_paper":"https://pith.science/paper/JDDVACLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.02958&json=true","fetch_graph":"https://pith.science/api/pith-number/JDDVACLBSNCKOREBI76GEIY7YZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JDDVACLBSNCKOREBI76GEIY7YZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ/action/storage_attestation","attest_author":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ/action/author_attestation","sign_citation":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ/action/citation_signature","submit_replication":"https://pith.science/pith/JDDVACLBSNCKOREBI76GEIY7YZ/action/replication_record"}},"created_at":"2026-05-18T00:28:28.788762+00:00","updated_at":"2026-05-18T00:28:28.788762+00:00"}