ON THE DOMAIN OF THE CONVERGENCE OF TAYLOR-DIRECHLET SERIES WITH COMPLEX EXPONENTS

Abstract

The article deals with Dirichlet series of the form F(z) = Σ+∞ k=0 akezλk , as well as Taylor-Dirichlet series of the form F1(z) =+∞Σk=0 zmkakezλk , where (λk) is some sequence of pairwise different complex numbers, and mk is a sequence of non-negative integers, ak ∈ C. The main statements of the work are Statements 1–3 and relate to the description and relationship between the domains of convergence, absolute convergence, and the domains of existence of the maximum term of the above series F and F1.