SINGU LAR POINTS OF THE SUM OF A SERIES OF EXPONENTIAL MONOMIALS ON THE BOUNDARY OF THE CONVERGENCE DOMAIN

摘要

Singular points for the sum of a series of exponential monomials are studied. The main statement contains results of Hadarnard, Fabry, V. Bernstein, Polya, Carlson and Landau as particular cases. Moreover, a special function is constructed that has no singular points on the boundary of the convergence domain of its series. This function generalizes a certain special function in the theory of Dirichlet series to the case of series of exponential monomials. The existence of this special function shows the necessity of a condition in the main theorem; in V. Bernstein's theorem, a similar role is played by the requirement that the condensation index should be equal to zero.