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The B\\\"ottcher coordinate of a power series $\\varphi(x)\\in x^m + x^{m+1}R[\\![x]\\!]$ is the unique power series $f_\\varphi(x)\\in x+x^2K[\\![x]\\!]$ satisfying $\\varphi\\circ f_\\varphi(x) = f_\\varphi(x^m)$. In this paper we study the integrality properties of the coefficients of $f_\\varphi(x)$, partly for their intrinsic interest and partly for potential applications to $p$-adic dynamics. Results include: (1) If $p$ is prime and $R=\\mathbb Z_p$ and $\\varphi(x)\\in x^p + px^{p+1}R[\\![x]\\!]$, then $f_\\varphi(x)\\in R["},"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":"1708.09275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-30T13:54:02Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"55eaaa8b0fafcbbf1f9e98f5bbc1437a1fbfd7599b40cb597cd795de69dc72c8","abstract_canon_sha256":"549f52545b35a212b4a63b3fcfd9a36aaaece98edea4567f04fba09a701cb632"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:48.438251Z","signature_b64":"yla3fhyQUWY7liFYE9el3A6qSkMo0O+E+6sNDLaC6bD2vq88vdutjIieYgy3MlpN3skySAGafiy46GbxGm/BAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"512f0b75082b0a0875412c3ec32ec03a0eba78f5716dc5c5079c0abad48401f1","last_reissued_at":"2026-05-18T00:33:48.437485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:48.437485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrality properties of B\\\"ottcher coordinates for one-dimensional superattracting germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Adriana Salerno, Joseph H. Silverman","submitted_at":"2017-08-30T13:54:02Z","abstract_excerpt":"Let $R$ be a ring of characteristic $0$ with field of fractions $K$, and let $m\\ge2$. The B\\\"ottcher coordinate of a power series $\\varphi(x)\\in x^m + x^{m+1}R[\\![x]\\!]$ is the unique power series $f_\\varphi(x)\\in x+x^2K[\\![x]\\!]$ satisfying $\\varphi\\circ f_\\varphi(x) = f_\\varphi(x^m)$. In this paper we study the integrality properties of the coefficients of $f_\\varphi(x)$, partly for their intrinsic interest and partly for potential applications to $p$-adic dynamics. 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