The Growth of an Entire Function Represented by Lacunary and Generalized Dirichlet Series

Abstract:

      For an entire function represented by finite order and generalized dirichlet series, we introduce order $\rho_R$ (type $\tau_R$ ) and study the relation between order $\rho_R$ (type $\tau_R$ ) and order $\rho_L$ (type $\tau_L$ ) in any horizontal line respectively. Applying to Taylor series, we can get analogous results.