Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(4): 1159-1171

Online first article May 18, 2017      Printed July 31, 2017

https://doi.org/10.4134/BKMS.b160238

Copyright © The Korean Mathematical Society.

Two meromorphic functions sharing four pairs of small functions

Van An Nguyen and Duc Quang Si

Banking Academy, Hanoi National University of Education

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\"{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\"{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\"{o}bius-transformation between such $f$ and $g$ is given. Our results are improvement of some recent results.

Keywords: meromorphic function, small function, M\"{o}bius transformation

MSC numbers: Primary 32H30, 32A22; Secondary 30D35