# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsmathscidoc:1701.03024

Arkiv for Matematik, 50, (1), 89-110, 2010.1
We show that a family $\mathcal{F}$ of analytic functions in the unit disk ${\mathbb{D}}$ all of whose zeros have multiplicity at least$k$and which satisfy a condition of the form $$f^n(z)f^{(k)}(xz)\ne1$$ for all $z\in{\mathbb{D}}$ and $f\in\mathcal{F}$ (where$n$≥3,$k$≥1 and 0<|$x$|≤1) is normal at the origin. The proof relies on a modification of Nevanlinna theory in combination with the Zalcman–Pang rescaling method. Furthermore we prove the corresponding Picard-type theorem for entire functions and some generalizations.
@inproceedings{jürgen2010a,
title={A normality criterion involving rotations and dilations in the argument},
author={Jürgen Grahl},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203631886379015},
booktitle={Arkiv for Matematik},
volume={50},
number={1},
pages={89-110},
year={2010},
}
Jürgen Grahl. A normality criterion involving rotations and dilations in the argument. 2010. Vol. 50. In Arkiv for Matematik. pp.89-110. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203631886379015.