{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TC3P2243EFJDZ5A2BUE7BPPWHT","short_pith_number":"pith:TC3P2243","schema_version":"1.0","canonical_sha256":"98b6fd6b9b21523cf41a0d09f0bdf63cfb33b5f3c3afccf39aff2ccdda711251","source":{"kind":"arxiv","id":"1908.00730","version":1},"attestation_state":"computed","paper":{"title":"Zeros of repeated derivatives of random polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dong Yao, Renjie Feng","submitted_at":"2019-08-02T07:42:12Z","abstract_excerpt":"It has been shown that zeros of Kac polynomials $K_n(z)$ of degree $n$ cluster asymptotically near the unit circle as $n\\to\\infty$ under some assumptions. This property remains unchanged for the $l$-th derivative of the Kac polynomials $K^{(l)}_n(z)$ for any fixed order $l$. So it's natural to study the situation when the number of the derivatives we take depends on $n$, i.e., $l=N_n$. We will show that the limiting global behavior of zeros of $K_n^{(N_n)}(z)$ depends on the limit of the ratio $N_n/n$. In particular, we prove that when the limit of the ratio is strictly positive, the property "},"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":"1908.00730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-02T07:42:12Z","cross_cats_sorted":[],"title_canon_sha256":"8008af7921521e610f500a6749f020a0cc4b9fbb913648fb8400b1066a20072e","abstract_canon_sha256":"1694b40bcaedf331c3da73b289658256dd1efe5d85d02abca79c7599d720b111"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:08.967168Z","signature_b64":"8Yt0zphYyXCLERIof7+tvQGGuLgJVhELHEJj5ixma6x/9uuZWXNYx3eLmB6fsLTNIy8pqxVmd/n7eVu28lxPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98b6fd6b9b21523cf41a0d09f0bdf63cfb33b5f3c3afccf39aff2ccdda711251","last_reissued_at":"2026-07-04T23:51:08.966758Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:08.966758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zeros of repeated derivatives of random polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dong Yao, Renjie Feng","submitted_at":"2019-08-02T07:42:12Z","abstract_excerpt":"It has been shown that zeros of Kac polynomials $K_n(z)$ of degree $n$ cluster asymptotically near the unit circle as $n\\to\\infty$ under some assumptions. This property remains unchanged for the $l$-th derivative of the Kac polynomials $K^{(l)}_n(z)$ for any fixed order $l$. So it's natural to study the situation when the number of the derivatives we take depends on $n$, i.e., $l=N_n$. We will show that the limiting global behavior of zeros of $K_n^{(N_n)}(z)$ depends on the limit of the ratio $N_n/n$. In particular, we prove that when the limit of the ratio is strictly positive, the property "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00730","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00730/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.00730","created_at":"2026-07-04T23:51:08.966825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.00730v1","created_at":"2026-07-04T23:51:08.966825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00730","created_at":"2026-07-04T23:51:08.966825+00:00"},{"alias_kind":"pith_short_12","alias_value":"TC3P2243EFJD","created_at":"2026-07-04T23:51:08.966825+00:00"},{"alias_kind":"pith_short_16","alias_value":"TC3P2243EFJDZ5A2","created_at":"2026-07-04T23:51:08.966825+00:00"},{"alias_kind":"pith_short_8","alias_value":"TC3P2243","created_at":"2026-07-04T23:51:08.966825+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/TC3P2243EFJDZ5A2BUE7BPPWHT","json":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT.json","graph_json":"https://pith.science/api/pith-number/TC3P2243EFJDZ5A2BUE7BPPWHT/graph.json","events_json":"https://pith.science/api/pith-number/TC3P2243EFJDZ5A2BUE7BPPWHT/events.json","paper":"https://pith.science/paper/TC3P2243"},"agent_actions":{"view_html":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT","download_json":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT.json","view_paper":"https://pith.science/paper/TC3P2243","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.00730&json=true","fetch_graph":"https://pith.science/api/pith-number/TC3P2243EFJDZ5A2BUE7BPPWHT/graph.json","fetch_events":"https://pith.science/api/pith-number/TC3P2243EFJDZ5A2BUE7BPPWHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT/action/storage_attestation","attest_author":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT/action/author_attestation","sign_citation":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT/action/citation_signature","submit_replication":"https://pith.science/pith/TC3P2243EFJDZ5A2BUE7BPPWHT/action/replication_record"}},"created_at":"2026-07-04T23:51:08.966825+00:00","updated_at":"2026-07-04T23:51:08.966825+00:00"}