Dirichlet级数及随机Dirichlet级数在水平直线上的增长性

该文研究Dirichlet及随机Dirichlet级数在水平直线或半直线上的增长性,包含关于Taylor级数的相应结果,例如下列简单结果:设Taylor级数F_(z)=sum from n=0 to ∞有收敛半径∞或1,其中0=μ_0<μ_n↑,μ_n∈N,sum from(1/μ_n)<∞.如果这级数有级ρ(在收敛半径是∞或1时,“级”的意义不同),那么在第一种情形。它在从原点出发的每条射线上有级p;在第二种情形,在单位圆盘的每条射线上有级ρ．

On the Growth of Dirichlet and Random DirichletSeries on Horizontal Lines

Abstract; In this paper we study the growth of Dirichlet and random Dirichlet series on horizontal lines or hall-lines. It contains corresponding results on Taylor series. For example,we have the following simple result:Lei the Taylor series F(z) =has a radius of convergence or 1, where 0 = If F(z) is of order p (For the two cases of the radius of convergence,the meanings of "order"are different. ) .then F(z) is of order p ,in the first case,on every ray from the origin,and in the second case,on every ray of the unit disk.