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arXiv · 1405.3742

A note on the value distribution of $f^l(f^{(k)})^n$

Jiang Yan·Huang Bin
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Abstract

Let $f$ be a transcendental meromorphic function in the complex plane $\mathbb{C}$, and $a$ be a nonzero complex number . We give quantitative estimates for the characteristic function $T(r,f)$ in terms of $N(r,1/(f^l(f^{(k)})^n-a))$, for integers $k$, $l$, $n$ greater than 1. We conclude that $f^l(f^{(k)})^n$ assumes every nonzero finite value infinitely often.

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Jiang Yan, Huang Bin. 2014-05-15. A note on the value distribution of $f^l(f^{(k)})^n$. https://arxiv.org/abs/1405.3742

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