相关论文: Nevanlinna theory and value distribution in the un…

Certain estimates involving the derivative $f\mapsto f'$ of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose of this study is to extend the usual Nevanlinna theory to a…

A parameter $c_0\in\mathbb C$ in the family of quadratic polynomials $f_c(z)=z^2+c$ is a critical point of a period $n$ multiplier, if the map $f_{c_0}$ has a periodic orbit of period $n$, whose multiplier, viewed as a locally analytic…

We establish an approximation of the activity current $T_c$ in the parameter space of a holomorphic family $f$ of rational functions having a marked critical point $c$ by parameters for which $c$ is periodic under $f$, i.e., is a…

In the moduli space of degree d polynomials, we prove the equidistribution of postcritically finite polynomials toward the bifurcation measure. More precisely, using complex analytic arguments and pluripotential theory, we prove the…

Let $f=(f_1,\ldots,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\lambda\in\mathbb{C}$ an eigenvalue of $f$ if there exists $v\in\mathbb{C}^n\backslash\{0\}$ with $f(v)=\lambda v$,…

We establish the equidistribution of the sequence of the averaged pullbacks of a Dirac measure at any value in $\mathbb{C}\setminus\{0\}$ under the derivatives of the iterations of a polynomials $f\in\mathbb{C}[z]$ of degree more than one…

Let $\Lambda$ be a quasi-projective variety and assume that, either $\Lambda$ is a subvariety of the moduli space $\mathcal{M}_d$ of degree $d$ rational maps, or $\Lambda$ parametrizes an algebraic family $(f_\lambda)_{\lambda\in\Lambda}$…

In the paper, using Nevanlinna's value distribution theory of meromorphic functions in $\mathbb{C}^m$, we study for the existence of entire solutions $f$ in $\mathbb{C}^m$ of the following algebraic partial differential equation…

We prove that unicritical polynomials $f(z)=z^d+c$ which are semihyperbolic, i.e., for which the critical point $0$ is a non-recurrent point in the Julia set, are uniformly expanding on the Julia set with respect to the metric $\rho(z)…

Fix $d\geq2$ and let $f_{t}(z)=z^{d}+t$ be the family of polynomials parameterized by $t\in\mathbb{C}$. In this article, we will show that there exists a constant $C(d)$ such that for any $a,b\in\mathbb{C}$ with $a^{d}\neq b^{d}$, the…

This paper investigates the value distribution and growth properties of linear total differential polynomials $\mathcal{L}_k[D]f$ for meromorphic functions in several complex variables $\mathbb{C}^n$. By extending the classical Milloux…

Let {f_t} be any algebraic family of rational maps of a fixed degree, with a marked critical point c(t). We first prove that the hypersurfaces of parameters for which c(t) is periodic converge as a sequence of positive closed (1,1) currents…

The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series…

In the moduli space of degree d polynomials, the set Per\_n(w) of classes [f] for which f admits a cycle of exact period n and multiplier w is known to be an algebraic hypersurface. We prove that, given a complex number w, these…

In the family of degree $d$ polynomials the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier $e^{i\theta}$ are shown to equiditribute the bifurcation current.

The period polynomial $r_f(z)$ for an even weight $k\geq 4$ newform $f\in S_k(\Gamma_0(N))$ is the generating function for the critical values of $L(f,s)$. It has a functional equation relating $r_f(z)$ to $r_f\left(-\frac{1}{Nz}\right)$.…

Let $p_n$ be the characteristic polynomial of an $n \times n$ random matrix drawn from one of the compact classical matrix groups. We show that the critical points of $p_n$ converge to the uniform distribution on the unit circle as $n$…

Let $f$ be a holomorphic endomorphism of $\mathbb P^k$ of algebraic degree $d\geq 2$. We show that the periodic points of $f$ of period $n$ equidistribute towards the equilibrium measure of $f$ exponentially fast as $n$ tends to infinity.…

We formulate an abstract notion of equidistribution for families of $\lambda$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $\sigma$-moment generating functions…

We prove that Misiurewicz parameters with prescribed combinatorics and hyperbolic parameters with (d - 1) distinct attracting cycles with given multipliers are equidistributed with respect to the bifurcation measure in the moduli space of…