{"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. 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["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09275","kind":"arxiv","version":2},"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"}