On meromorphic functions without Julia directions

Tien-Yu Peter Chern

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On meromorphic functions without Julia directions

Tien-Yu Peter Chern

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Abstract

It is proved that for any positive number $λ$, $1<λ<2$; there exists a meromorphic function $f$ with logarithmic order $λ$= $\displaystyle\limsup_{r\to+\infty}\frac{\log T(r,f)}{\log\log r}$ such that $f$ has no Julia directions, where $T(r,f)$ is the Nevanlinna characteristic function of $f$. (Note that A. Ostrowski has proved a {\it similar} result for $λ=2$ in 1926.)

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BibTeX RIS

Tien-Yu Peter Chern. 2006-11-11. On meromorphic functions without Julia directions. https://arxiv.org/abs/math/0604244

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