Uniqueness Theorem of Algebroidal Functions in an Angular Domain

Abstract:

      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 $M(z)$).