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### Canonical products of infinite order.

Journal für die reine und angewandte Mathematik

### Proof of a Conjecture of Gross Concerning Fix-points.

Mathematische Zeitschrift

### On the singularities of the inverse to a meromorphic function of finite order.

Revista Matemática Iberoamericana

Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f, except at most 2ρ of them, is a limit point of critical values of f. We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f'fn with n ≥ 1 takes every finite non-zero value infinitely often. This proves a conjecture of Hayman....

### Transcendency of Local Conjugacies in Complex Dynamics and Transcendency of their Values.

Manuscripta mathematica

### Fixed points of composite entire and quasiregular maps.

For an entire function $f$ let $N\left(z\right)=z-f\left(z\right)/{f}^{\prime }\left(z\right)$ be the Newton function associated to $f$. Each zero $\xi$ of $f$ is an attractive fixed point of $N$ and is contained in an invariant component of the Fatou set of the meromorphic function $N$ in which the iterates of $N$ converge to $\xi$. If $f$ has an asymptotic representation $f\left(z\right)\sim exp\left(-{z}^{n}\right),\phantom{\rule{0.166667em}{0ex}}n\in ℕ$, in a sector $|argz|<\epsilon$, then there exists an invariant component of the Fatou set where the iterates of $N$ tend to infinity. Such a component is called an invariant Baker domain. A question in the opposite...