角域内代数体函数的唯一性定理

Let W (z) and M(z) be v-valued and k-valued algebroidal functions respectively,(θ) be a b-cluster line of order ∞ (or ρ(r)) of W (z) (or M(z)).It is shown that W (z) ≡ M(z) provided E(a j ,W (z)) = E(a j ,M(z)) (j = 1,...,2v + 2k + 1) holds in the angular domain Ω(θ- δ,θ + δ),where b,a j (j = 1,...,2v + 2k + 1) are complex constants.The same results are obtained for the case that (θ) is a Borel direction of order ∞ (or ρ(r)) of W (z) (or M(z)).

Uniqueness Theorem of Algebroidal Functions in an Angular Domain

Let $W(z)$ and $M(z)$ be $v$-valued and $k$-valued algebroidal functions respectively, $\triangle(\theta)$ be a $b$-cluster line of order $\infty$ (or $\rho(r)$) of $W(z)$ (or $M(z)$). It is shown that $W(z)\equiv M(z)$ provided $\overline{E}(a_j,W(z))=\overline{E}(a_j,M(z))~(j=1,\ldots,2v+2k+1)$ holds in the angular domain $\Omega(\theta-\delta,\theta+\delta)$, where $b,a_j~(j=1,\ldots,2v+2k+1)$ are complex constants. The same results are obtained for the case that $\triangle(\theta)$ is a Borel direction of order $\infty$ (or $\rho(r)$) of $W(z)$ (or $M(z)$).