亚纯函数微分多项式分担多项式的唯一性

研究了亚纯函数的微分多项式f~nf~′和g~ng~′IM分担一个多项式P(z)的唯一性问题,证明了当n22且多项式P(z)的次数小于等于n时,则f(z)=tg(z),或者f(z)=λ_1e~(λ∫P(z)dz),g(z)=2e~(-λ∫P(z)dz),其中,t,λ1λ2,λ为常数。

Uniqueness of differential polynomials of meromorphic functions sharing a polynomial

The uniqueness of differential polynomials of meromorphic functions ${f^n}f''$ and ${g^n}g''$ IM sharing a polynomial $P(z)$ was studied. If $n > 22$ and the degree of $P(z)$ is not more than $n$, then $f(z) = tg(z)$, or $f(z) = {\lambda _1}{{\rm{e}}^{{\rm{\lambda}} \int {{{P}}({{z}}){{{\rm d}z}}} }}$, $g(z) = {\lambda _2}{{\rm{e}}^{ - {\rm{\lambda}} \int {{{P}}({{z}})} {\rm d}z}}$, where $t$, ${\lambda _1},{\lambda _2}$, $\lambda $ are constants.