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The first is \"Taylor domination\" property for $f(z)$ in the complex disk $D_R$, which is an inequality of the form \\[ |a_{k}|R^{k}\\leq C\\ \\max_{i=0,\\dots,N}\\ |a_{i}|R^{i}, \\ k \\geq N+1. \\] The second approach is based on a possibility to generate $a_k$ via recurrence relations. Specifically, we consider linear non-stationary recurrences of the form \\[ a_{k}=\\sum_{j=1}^{d}c_{j}(k)\\cdot a_{k-j},\\ \\ k=d,d+1,\\dots, \\] with uniformly bounded coefficients.\n  In t"},"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":"1411.7629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-27T15:44:07Z","cross_cats_sorted":[],"title_canon_sha256":"fb966aa70bf7cffbdaf0482ca01a0b300f9a8856924c76d8ce69d104fe499b70","abstract_canon_sha256":"00f91e6aab2d08926483169d29d564b723d75b13c871b3fa6a9ba1912f4ba6c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:37.548878Z","signature_b64":"eDWGf90aFYaEv6Msp28GwTxFn3FSVsUJ1QetUlY7jet4UukHr4SDxNLqoc1wkFnPZyR7B/hn5APG6IUzVqGFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"650d6add24d524cbaa66b8a54f7127d079af5e636e02ce2e0865e85ae59baf30","last_reissued_at":"2026-05-18T02:32:37.548415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:37.548415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Taylor Domination, Difference Equations, and Bautin Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Batenkov, Yosef Yomdin","submitted_at":"2014-11-27T15:44:07Z","abstract_excerpt":"We compare three approaches to studying the behavior of an analytic function $f(z)=\\sum_{k=0}^\\infty a_kz^k$ from its Taylor coefficients. 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