On Properties of Zero Points and Poles of K-Bianalytic Functions
Junyou Ni
Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310012, China.
Hongliang Li *
Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310012, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we first prove that the set of zero points of a nonzero K-bianalytic function \(f(z)=\bar{z}(k)\phi_1(z(k))+\phi(z(k)), z\) \(\epsilon D\), is not a region and the set of the second zero points has no accumulated point. Second, a sufficient and necessary condition is given for a K-bianalytic function to have a zero arc which has a parameter equation \(\bar{z}(k)=\gamma(z(k))\) where \(\gamma\) is an analytic function in a region D(k). Finally, the traits of a K-bianalytic function which has a zero arc, even straight, one of whose ends is a \((c_1,c_2)-\)th pole at z = 0, are discussed. Some examples are also shown for our topic.
Keywords: Zero points, poles, K-bianalytic functions