A probabilistic approach to the wiman—valiron theory for functions of several complex entire

Abstract

The classical theorems of Wiman Valiron and Clunie on the relationship between the maximum modulus, maximum term and central index of an entire function of one complex variable are generalized to the case of several complex variables. The method of proof is based on the probabilistic approach of Rosenbloom along with some new results on exponential families. The ideas presented should also allow extensions of the theory to analytic functions defined on arbitrary domains and represented by power series, Dirichiet series or general Laplace transforms.

AMS No:

• 32A15