**Yûsuke Okuyama** ^{[a]}

*Nevanlinna theory and value distribution in the unicritical polynomials family
*

**Pages:**

**Received:** 26 April 2017

**Accepted in revised form:** 14 March 2018

**Mathematics Subject Classification (2010):** Primary 37F45; Secondary 30D35.

**Keywords:** Unicritical polynomials family, superattracting periodic point, equidistribution, Nevanlinna theory.

**Author address:**

[a]: Division of Mathematics, Kyoto Institute of Technology Sakyo-ku, Kyoto 606-8585 Japan

**Abstract:**
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 play key roles.

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