Proceedings of the Japan Academy, Series A, Mathematical Sciences

Derivatives of meromorphic functions and sine function

Pai Yang, Xiaojun Liu, and Xuecheng Pang

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Abstract

In the paper, we take up a new method to prove the following result. Let $f$ be a meromorphic function in the complex plane, all of whose zeros have multiplicity at least $k+1$ ($k\geq 2$) and all of whose poles are multiple. If $T(r,\sin z)=o\{T(r,f(z))\}$ as $n\rightarrow\infty$, then $f^{(k)}(z)-\sin z$ has infinitely many zeros.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 9 (2015), 129-134.

Dates
First available in Project Euclid: 29 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1446124156

Digital Object Identifier
doi:10.3792/pjaa.91.129

Mathematical Reviews number (MathSciNet)
MR3418201

Zentralblatt MATH identifier
1337.30045

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 30D45: Bloch functions, normal functions, normal families

Keywords
Meromorphic function normal familiy sine function

Citation

Yang, Pai; Liu, Xiaojun; Pang, Xuecheng. Derivatives of meromorphic functions and sine function. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 9, 129--134. doi:10.3792/pjaa.91.129. https://projecteuclid.org/euclid.pja/1446124156


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References

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