Radically distributed value and normal families of meromorphic functions

Jianming QI; Guowei ZHANG; Wenjun YUAN

doi:10.1007/s11464-014-0357-7

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Front. Math. China ›› 2014, Vol. 9 ›› Issue (2) : 355-376. DOI: 10.1007/s11464-014-0357-7

RESEARCH ARTICLE

Radically distributed value and normal families of meromorphic functions

Jianming QI¹^,² ,
Guowei ZHANG³ ,
Wenjun YUAN²^,⁴

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Abstract

We establish several upper-bound estimates for the growth of meromorphic functions with radially distributed value. We also obtain a normality criterion for a class of meromorphic functions, where any two of whose differential polynomials share a non-zero value. Our theorems improve some previous results.

Keywords

Meromorphic function / Nevanlinna theory / normal family / angular characteristic function / radially distributed value

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Jianming QI, Guowei ZHANG, Wenjun YUAN. Radically distributed value and normal families of meromorphic functions. Front. Math. China, 2014, 9(2): 355‒376 https://doi.org/10.1007/s11464-014-0357-7

References

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[1]	BaernsteinA. Proof of Edrei’s spread conjecture. Proc Lond Math Soc, 1973, 26: 418-434 CrossRef Google scholar

[2]	BergweilerW, EremenkoA. On the singularities of the inverse to a meromorphic function of finite order. Rev Mat Iberoam, 1995, 11(2): 355-373 CrossRef Google scholar

[3]	ChenS J, LinW C, ChenJ F. on the growth of meromorphic functions with a radially distributed value. Indian J Pure Appl Math, 2011, 42(1): 53-70 CrossRef Google scholar

[4]	ChuangC T. Sur la comparaison de la croissance d’une fonction méromorphe et de celle de sa dérivée. Bull Sci Math, 1951, 75: 171-190

[5]	EdreiA. Meromorphic functions with three radially distributed values. Trans Amer Math Soc, 1955, 78: 276-293 376 Jianming QI et al.

[6]	EdreiA. Sums of deficiencies of meromorphic function. J Analyse Math, 1965, 14: 79-107 CrossRef Google scholar

[7]	FangM L, ZalcmanL. On value distribution of f + α(f′)ⁿ. Sci China Ser A, 2008, 38(3): 279-285

[8]	Gol’dbergA A, OstrovskiiI V. The Distribution of Values of Meromorphic Functions. Moscow: Izdat Nauka, 1970 (in Russian)

[9]	HaymanW K. Meromorphic Functions. Oxford: Clarendon Press, 1964

[10]	HaymanW K, MilesJ. On the growth of a meromorphic function and its derivatives. Complex Variables, 1989, 12: 245-260 CrossRef Google scholar

[11]	HeY Z, XiaoX Z. Algebroid Functions and Ordinary Differential Equations. Beijing: Science Press, 1988 (in Chinese)

[12]	LaineI. Nevanlinna Theory and Complex Differential Equations. Berlin: de Gruyter, 1993

[13]	NevanlinnaR. Uber die eigenschaften meromorphic funktionen in einem winkelraum. Acta Soc Sci Feen, 1925, 50: 1-45

[14]	PangX C, ZalcmanL. Normal families and shared values. Bull Lond Math Soc, 2000, 32: 325-331 CrossRef Google scholar

[15]	QiJ M, ZhuT Y. Some normal criteria about shared values with their multiplicity zeros. Abstr Appl Anal, 2010, CrossRef Google scholar

[16]	XuY, WuF Q, LiaoL W. Picard values and normal families of meromorphic functions. Proc Roy Soc Edinburgh Sect A, 2009, 139: 1091-1099 CrossRef Google scholar

[17]	YangL. Borel directions of meromorphic functions in an angular domain. Sci China, 1979, (Math Ser I): 149-163

[18]	YangL, YangC C. Angular distribution of values of f f′. Sci China Ser A-Math, 1994, 37: 284-294

[19]	ZalcmanL. A heuristic principle in complex function theory. Amer Math Monthly, 1975, 82: 813-817 CrossRef Google scholar

[20]	ZhengJ H. On transcendental meromorphic functions with radially distributed values. Sci China Ser A-Math, 2004, 47: 401-416 CrossRef Google scholar