Hiroshima Mathematical Journal

A note on the value distribution of $f^1(f^{(k)})^n$

Yan Jiang and Bin Huang

Full-text: Open access

Abstract

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

Article information

Source
Hiroshima Math. J., Volume 46, Number 2 (2016), 135-147.

Dates
Received: 8 May 2014
Revised: 15 October 2014
First available in Project Euclid: 12 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1471024945

Digital Object Identifier
doi:10.32917/hmj/1471024945

Mathematical Reviews number (MathSciNet)
MR3536992

Zentralblatt MATH identifier
1355.30030

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory

Keywords
Transcendental meromorphic function deficiency

Citation

Jiang, Yan; Huang, Bin. A note on the value distribution of $f^1(f^{(k)})^n$. Hiroshima Math. J. 46 (2016), no. 2, 135--147. doi:10.32917/hmj/1471024945. https://projecteuclid.org/euclid.hmj/1471024945


Export citation