[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b160238

TWO MEROMORPHIC FUNCTIONS SHARING FOUR PAIRS OF SMALL FUNCTIONS

Nguyen, Van An (Division of Mathematics Banking Academy)
Si, Duc Quang (Department of Mathematics Hanoi National University of Education)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1159-1171 More about this Journal

Abstract

The purpose of this paper is twofold. The first is to show that two meromorphic functions f and g must be linked by a quasi- $M{\ddot{o}}bius$ transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi- $M{\ddot{o}}bius$ transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by 4, where all zeros with multiplicities at least k > 865 are omitted. Moreover the explicit $M{\ddot{o}}bius$ -transformation between such f and g is given. Our results are improvement of some recent results.

Keywords

meromorphic function; small function; $M{\ddot{o}}bius$ transformation;

Citations & Related Records

Reference

1	T. Czubiak and G. Gundersen, Meromorphic functions that share pairs of values, Complex Var. Elliptic Equ. 34 (1997), no. 1-2, 35-46. DOI
2	P. Li and C. C. Yang, On two meromorphic functions that share pairs of small functions, Complex Var. Elliptic Equ. 32 (1997), no. 2, 177-190. DOI
3	P. Li and Y. Zhang, Meromorphic functions that share some pair of small functions, Kodai Math. J. 32 (2009), no. 1, 130-145. DOI
4	J. Noguchi, A note on entire pseudo-holomorphic curves and the proof of Cartan-Nochka's theorem, Kodai Math. J. 28 (2005), no. 2, 336-346. DOI
5	J. Noguchi and T. Ochiai, Introduction to Geometric Function Theory in Several Complex Variables, Trans. Math. Monogr. 80, Amer. Math. Soc., Providence, Rhode Island, 1990.
6	S. D. Quang, Two meromorphic functions share some pairs of small functions, Complex Anal. Oper. Theory 7 (2013), no. 4, 1357-1370. DOI
7	S. D. Quang and L. N. Quynh, Two meromorphic functions sharing some pairs of small functions regardless of multiplicities, Internat. J. Math. 25 (2014), no. 2, 1450014, 16 pp.
8	D. D. Thai and S. D. Quang, Second main theorem with truncated counting function in several complex variables for moving targets, Forum Math. 20 (2008), no. 1, 163-179. DOI
9	K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), no. 2, 225-294. DOI
10	J. Zhang and L. Yang, Meromorphic functions sharing pairs of small functions, Math. Slovaca 65 (2015), no. 1, 93-102. DOI
11	H. Z. Cao and T. B. Cao, Two meromorphic functions share some pairs of small functions with truncated multiplicities, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 6, 1854-1864.