Order theory for isolated points of monogenic functions

Abstract.

In this paper we discuss problems related to the value distribution of some special meromorphic functions in Clifford analysis. With a generalized Argument principle we describe orders of isolated a-points of a monogenic function. We prove a generalized version of Rouché’s theorem. Further, we observe that the generalized elliptic functions in Clifford analysis play a special role with respect to value distributional questions. In particular, we discuss analogs to the classical Liouville theorems. The Argument principle will be exploited to show that the sum of the orders of all isolated a-points of a generalized elliptic function that has only isolated poles vanishes.