Some Problems Of Algebroid Functions

It's still imperfect about algebroid function, such as the relationship between the growth of algebroid function and the growth of irreducible equation'coefficient, which defined the algebroid function. What's more, we wonder whether there are some qualities about algebroid function corresponding to meromorphic func-tion,specially, concerning deficiency, characteristic function,differential polynomial and so on. This thesis devoted to study the above problems.The article can be divided into five sections.In the first part, we discussed the relationship between the growth of algebroid function and the growth of irreducible equation'coefficient, which defined the algebroid function.In the second part, we studied the close relationship between algebroid function' deficiency and characteristic function, then we compared the function's characteristic function to its derivative' characteristic function. We also gave a new definition of deficiency of algebroid functions and discussed their applications.In the third part, we proved an equality about algebroid function's differential polynomial.In the fourth part, we simplified the Xiong Qinglai's inequality, which has been generalized by He Yuzhang.Finally,we rectified the errors in some documents and improved them.