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Finiteness of meromorphic functions on an annulus sharing four values regardless of multiplicity

Duc Quang SiAn Hai Tran — 2020

Mathematica Bohemica

This paper deals with the finiteness problem of meromorphic funtions on an annulus sharing four values regardless of multiplicity. We prove that if three admissible meromorphic functions f 1 , f 2 , f 3 on an annulus 𝔸 ( R 0 ) share four distinct values regardless of multiplicity and have the of positive counting function, then f 1 = f 2 or f 2 = f 3 or f 3 = f 1 . This result deduces that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicity truncated to level 2 and sharing other three...

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