SOME OLD (UNSOLVED) AND NEW PROBLEMS AND CONJECTURES ON FUNCTIONAL EQUATIONS OF ENTIRE AND MEROMORPHIC FUNCTIONS

摘要

The purpose for posing these old and new problems and conjectures arised instudying the Nevanlinna's value distribution theory and its applications is to stim-ulate peers' interest to study further of the theory and properties of entire andmeromorphic functions of one complex variable. Also be reminded that one cancarry the studies to similar problems and conjectures entire and meromorphic func-tions of several complex variables as well as that of p-adic complex variables. Forsimplicity , here we shall address the problems and conjectures for (non-constant)entire or meromorphic functions of one complex variable only, and most of themwere proposed by the present author and his co-workers earlier. We refer the readerto [ 3 ] for the Nevanlinna's theory and its associated notations. Problems and con-jectures will be stated in three different topics : 1.Factorization and fixed points ofentire functions, 2. Dynamics of two permutable entire functions, and 3. Functionalequations of Diophantine type over functions field. Sources, definitions, and resultsrelevant to these problems and conjectures will be stated or cited, with references.