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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.
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참고문헌 (11)
참고문헌 신청
H. Z. Cao / 2014 / Two meromorphic functions share some pairs of small func-tions with truncated multiplicities / Acta Math. Sci. Ser. B Engl. Ed 34(6):1854~1864
T. Czubiak / 1997 / Meromorphic functions that share pairs of values / Complex Var. Elliptic Equ 34(1-2):35~46
P. Li / 1997 / On two meromorphic functions that share pairs of small functions / Complex Var. Elliptic Equ 32(2):177~190
P. Li / 2009 / Meromorphic functions that share some pair of small functions / Kodai Math. J 32(1):130~145
J. Noguchi / 2005 / A note on entire pseudo-holomorphic curves and the proof of Cartan-Nochka’s theorem / Kodai Math. J 28(2):336~346
T. Czubiak / 1997 / Meromorphic functions that share pairs of values / Complex Var. Elliptic Equ 34(1-2):35~46
P. Li / 1997 / On two meromorphic functions that share pairs of small functions / Complex Var. Elliptic Equ 32(2):177~190
P. Li / 2009 / Meromorphic functions that share some pair of small functions / Kodai Math. J 32(1):130~145
J. Noguchi / 2005 / A note on entire pseudo-holomorphic curves and the proof of Cartan-Nochka’s theorem / Kodai Math. J 28(2):336~346
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