The Research On The Uniqueness Of Meromorphic Function

This paper is focused on studying the uniqueness problem of entire functions which shares one value, basing on the Nevanlinna theory. Also, we improve a result which Young had proved and extend a conclusion. We discuss them in five sections.Firstly, we mainly introduce the basic definitions, fundamental theorems of Nevanlinna's value distribution theory and some symbols in common use.Secondly, we prove the equations f⁽ⁿ⁾-e^αf = Q and f⁽ⁿ⁺¹⁾ - e^βf = Q (Q is apolynomial, q is the times, n >q)have no common result, which is an extent of a result from Gundersen and Yang.In the third part, we investigate the problem of F = fⁿ(f-1)²f' andG = gⁿ (g-1)²g' share 1 CM.Finally, we study the uniqueness problem of entire functions, and gain a new result. Moreover, the result contains the related result.