分担集合的多项式的惟一性
The Uniqueness of Polynomial Sharing a Set

DOI: 10.12677/PM.2013.35045, PP. 295-299

Keywords: 多项式；分担值；CM分担；惟一性
Polynomial, Shared Value, CM Sharing, Uniqueness

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文研究了Gross在1976年所提出的一个惟一性问题关于多项式的情形，证明了存在三个元素的集合S，使得对于任何两个非常数多项式f和g，如果f, g CM分担S，则。并且集合S的基数3是最佳的。
>This paper studied the uniqueness of polynomial posed by Gross in 1976, and proved that there exists a set S with 3 elements such that for any two non-constant polynomials f and g, if f and g share S CM, then . And the number 3 of the set S is best possible.

References

[1]	R. Nevanlinna. Le Thérème de picard—Borel et la théorie des fonctions méromorphes. Paris: Gauthiervillars, 1929.
[2]	F. Gross. Factorization of meromorphic functions and some open problems, complex analysis. Berlin: Springer, 1977: 51-67.
[3]	F. Gross, C. C. Yang. On preimage and range sets of meromorphic function. Proceedings of the Japan Academy of Mathematical Sciences, 1982, 58(1): 17-20.
[4]	仪洪勋. 具有三个公共值的亚纯函数[J]. 中国科学A辑, 1994, 24(11): 1137-1144.
[5]	H. X. Yi. A question of gross and the uniqueness of entire functions. Nagoya Mathematical, 1995, 138: 169-177.

Full-Text