Articles

TWO MEROMORPHIC FUNCTIONS SHARE SOME PAIRS OF SMALL FUNCTIONS WITH TRUNCATED MULTIPLICITIES

  • CAO Hong-Zhe
Expand
  • Department of Mathematics, Nanchang University, Nanchang 330031, China

Received date: 2013-05-14

  Revised date: 2013-11-04

  Online published: 2014-11-20

Supported by

This research was partly supported by the NSFC (11401291, 11101201), the NSF of Jiangxi (2012 2BAB211001) and NSF of ED of Jiangxi (GJJ13077).

Abstract

Using the techniques proposed in [3], we prove that two nonconstant meromor-phic functions f and g on C must be linked by a quasi-M¨obius transformation if they share some pairs of small functions with more precise truncated multiplicities, which improve and extend the results of Duc Quang Si.

Cite this article

CAO Hong-Zhe . TWO MEROMORPHIC FUNCTIONS SHARE SOME PAIRS OF SMALL FUNCTIONS WITH TRUNCATED MULTIPLICITIES[J]. Acta mathematica scientia, Series B, 2014 , 34(6) : 1854 -1864 . DOI: 10.1016/S0252-9602(14)60129-6

References

[1] Czubiak T, Gundersen G. Meromorphic functions that share pairs of values. Complex Variables and Elliptic Equations, 1997, 34: 35–46

[2] Cao T B, Yi H X. On the multiple values and uniqueness of meromorphic functions sharing small functions as targets. Bull Korean Math Soc, 2007, 4: 631–640

[3] Quang S D. Two meromorphic functions share some pairs of small functions. Complex Anal Oper Theory, 2013, 7: 1357–1370

[4] Li P, Zhang Y. Meromorphic functions that share some pair of small functions. Kodai Math, 2009, 32: 130–145

[5] Noguchi J. A note on entire pseudo holomorphic curves and the proof of Cartan-Nochka´s theorem. Kodai Math, 2005, 28: 336–346

[6] Ru M. Nevanlinna Theory and Its Relation to Diophantine Approximation. Singapore: World Science Pub, 2001

[7] Thai D D, Quang S D. Second main theorem with truncated counting function in several complex variables for moving targets. Forum Math, 2008, 20: 145–179

[8] Yamanoi K. The second main theorem for small functions and related problems. Acta Math, 2004, 192: 225–294

[9] Chen Z, Li Y, Yan Q. Uniqueness problem with truncated multiplicities of meromorphic mappings for moving targest. Acta Math Sci, 2007, 27(3): 625–634

Outlines

/