{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:UPG65J5EZWWVNZIZ22YVIRFL4P","short_pith_number":"pith:UPG65J5E","schema_version":"1.0","canonical_sha256":"a3cdeea7a4cdad56e519d6b15444abe3dc577d81d57905c919e101042dd08d13","source":{"kind":"arxiv","id":"1108.5412","version":1},"attestation_state":"computed","paper":{"title":"Radii of Starlikeness and Convexity of Analytic Functions Satisfying Certain Coefficient Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"V. Ravichandran","submitted_at":"2011-08-27T02:55:34Z","abstract_excerpt":"For $0\\leq \\alpha <1$, the sharp radii of starlikeness and convexity of order $\\alpha$ for functions of the form $f(z)=z+a_2z^2+a_3z^3+...$ whose Taylor coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\\leq b\\leq 1$, and $|a_n|\\leq n $, $M$ or $M/n$ ($M>0$) for $n\\geq 3$ are obtained. Also a class of functions related to Carath\\'eodory functions is considered."},"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":"1108.5412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-27T02:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"d4ca7659b8af302cbd5bc908356465f5596eeca70bb7343a019de4a11907e9c2","abstract_canon_sha256":"661575707be699aff7480ab56885954f0df8f1403756eb611a22fcee6ded6ab4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:37.555802Z","signature_b64":"+rSviF3AY31Kf/092I6L0Xl5ZG4rG+bZK9Z6WhKBd/Iz1+gFjm3ZZM3jzQt6DpkmwS+NwXxqpXHDTFBaTgAYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3cdeea7a4cdad56e519d6b15444abe3dc577d81d57905c919e101042dd08d13","last_reissued_at":"2026-05-18T04:14:37.555226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:37.555226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Radii of Starlikeness and Convexity of Analytic Functions Satisfying Certain Coefficient Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"V. Ravichandran","submitted_at":"2011-08-27T02:55:34Z","abstract_excerpt":"For $0\\leq \\alpha <1$, the sharp radii of starlikeness and convexity of order $\\alpha$ for functions of the form $f(z)=z+a_2z^2+a_3z^3+...$ whose Taylor coefficients $a_n$ satisfy the conditions $|a_2|=2b$, $0\\leq b\\leq 1$, and $|a_n|\\leq n $, $M$ or $M/n$ ($M>0$) for $n\\geq 3$ are obtained. Also a class of functions related to Carath\\'eodory functions is considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5412","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":"1108.5412","created_at":"2026-05-18T04:14:37.555326+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5412v1","created_at":"2026-05-18T04:14:37.555326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5412","created_at":"2026-05-18T04:14:37.555326+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPG65J5EZWWV","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPG65J5EZWWVNZIZ","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPG65J5E","created_at":"2026-05-18T12:26:42.757692+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/UPG65J5EZWWVNZIZ22YVIRFL4P","json":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P.json","graph_json":"https://pith.science/api/pith-number/UPG65J5EZWWVNZIZ22YVIRFL4P/graph.json","events_json":"https://pith.science/api/pith-number/UPG65J5EZWWVNZIZ22YVIRFL4P/events.json","paper":"https://pith.science/paper/UPG65J5E"},"agent_actions":{"view_html":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P","download_json":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P.json","view_paper":"https://pith.science/paper/UPG65J5E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5412&json=true","fetch_graph":"https://pith.science/api/pith-number/UPG65J5EZWWVNZIZ22YVIRFL4P/graph.json","fetch_events":"https://pith.science/api/pith-number/UPG65J5EZWWVNZIZ22YVIRFL4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P/action/storage_attestation","attest_author":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P/action/author_attestation","sign_citation":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P/action/citation_signature","submit_replication":"https://pith.science/pith/UPG65J5EZWWVNZIZ22YVIRFL4P/action/replication_record"}},"created_at":"2026-05-18T04:14:37.555326+00:00","updated_at":"2026-05-18T04:14:37.555326+00:00"}