{"paper":{"title":"Nevanlinna theory and value distribution in the unicritical polynomials family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Y\\^usuke Okuyama","submitted_at":"2018-02-08T05:51:58Z","abstract_excerpt":"In the space $\\mathbb{C}$ of the parameters $\\lambda$ of the unicritical polynomials family $f(\\lambda,z)=f_\\lambda(z)=z^d+\\lambda$ of degree $d>1$, we establish a quantitative equidistribution result towards the bifurcation current (indeed measure) $T_f$ of $f$ as $n\\to\\infty$ on the averaged distributions of all parameters $\\lambda$ such that $f_\\lambda$ has a superattracting periodic point of period $n$ in $\\mathbb{C}$, with a concrete error estimate for $C^2$-test functions on $\\mathbb{P}^1$. In the proof, not only complex dynamics but also a standard argument from the Nevanlinna theory pl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02723","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"}