Open AccessTwo meromorphic functions on annuli sharing some pairs of small functions or values
Author(s) -
Hongzhe Cao
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021770
Subject(s) - meromorphic function , mathematics , transformation (genetics) , pure mathematics , annulus (botany) , function (biology) , representation (politics) , combinatorics , chemistry , gene , biochemistry , botany , evolutionary biology , biology , politics , political science , law
In this paper, we prove that two admissible meromorphic functions on an annulus must be linked by a quasi-Möbius transformation if they share some pairs of small function with multiplicities truncated by $ 4 $. We also give the representation of Möbius transformation between two admissible meromorphic functions on an annulus if they share four pairs of values with multiplicities truncated by $ 4 $. In our results, the zeros with multiplicities more than a certain number are not needed to be counted if their multiplicities are bigger than a certain number.