We take up a new method to prove a Picard type theorem. Let f be a meromorphic function in the complex plane, whose zeros are multiple, and let R be a MSbius transformation. If limr→∞T（r,f）/r^2= ∞, then f＇（z） ...We take up a new method to prove a Picard type theorem. Let f be a meromorphic function in the complex plane, whose zeros are multiple, and let R be a MSbius transformation. If limr→∞T（r,f）/r^2= ∞, then f＇（z） = R（ez） has infinitely many solutions in the complex plane.展开更多
Let f（z） be a meromorphic function in the complex plane, whose zeros have multiplicity at least k ＋ 1 （k 〉 2）. If sin z is a small function with respect to f（z）, then f（k） （z） - P（z） sin z has infinitely...Let f（z） be a meromorphic function in the complex plane, whose zeros have multiplicity at least k ＋ 1 （k 〉 2）. If sin z is a small function with respect to f（z）, then f（k） （z） - P（z） sin z has infinitely many zeros in the complex plane, where P（z） is a nonzero polynomial of deg（P（z）） ≠ 1. Keywords Meromorphic function, Nevanlinna theory, Picard type theorem.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11501367, 11671191）
文摘We take up a new method to prove a Picard type theorem. Let f be a meromorphic function in the complex plane, whose zeros are multiple, and let R be a MSbius transformation. If limr→∞T（r,f）/r^2= ∞, then f＇（z） = R（ez） has infinitely many solutions in the complex plane.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11301140,11671191 and 11501367)China Postdoctoral Science Foundation(Grant No.2015M571726)the Project of Sichuan Provincial Department of Education(Grant No.15ZB0172)
文摘Let f（z） be a meromorphic function in the complex plane, whose zeros have multiplicity at least k ＋ 1 （k 〉 2）. If sin z is a small function with respect to f（z）, then f（k） （z） - P（z） sin z has infinitely many zeros in the complex plane, where P（z） is a nonzero polynomial of deg（P（z）） ≠ 1. Keywords Meromorphic function, Nevanlinna theory, Picard type theorem.
