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Under certain essential conditions, we prove the uniqueness of p(f) and P[f] when p(f) and P[f] share a with weight l greater than or equal to zero. Our result generalizes the results due to Zang and Lu, Banerjee and Majumder, Bhoosnurmath and Kabbur and answers a question of Zang and Lu."},"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":"1501.05092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-21T08:35:58Z","cross_cats_sorted":[],"title_canon_sha256":"082b93143b88061d7c5bd2a6d6edc59e97d836c6d4dbea2d381614a03a589dc3","abstract_canon_sha256":"dff704cdd319d5f226f1ff8929b1e98f66127c2eec069e5c45c4b2eb8dcaa663"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:43.857910Z","signature_b64":"+Wo91UKlac1PbVTrsfEuLyKKsckEvuPH33qZrtOvHO7R3sY7BG41x0gzvH9AXjNe8QL/Yr8XXJIiMXtsnj2aCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b46c96b01d60edd126413cddfad6113ed458b7258c9e29808286e475803d89cd","last_reissued_at":"2026-05-18T02:27:43.857180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:43.857180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of p(f) and P[f]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Banarsi Lal, Kuldeep Singh Charak","submitted_at":"2015-01-21T08:35:58Z","abstract_excerpt":"Let f be a non constant meromorphic function and a(not identically zero or infinity) be a meromorphic function satisfying T(r,a) = o(T(r,f)) as r tends to infinity, and p(z) be a polynomial of degree n greater than or equal to 1 with p(0) = 0. Let P[f] be a non constant differential polynomial of f. Under certain essential conditions, we prove the uniqueness of p(f) and P[f] when p(f) and P[f] share a with weight l greater than or equal to zero. 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