Dirichlet级数和随机Dirichlet级数的增长性

The growth of Dirichlet series and random Dirichlet series

研究全平面上部分零级和有限级Dirichlet级数及随机Dirichlet级数的系数和增长性之间的关系,并得到了当随机变量序列{Xn(ω)}满足一定条件时,部分零级和有限级随机Dirichlet级数在全平面所确定的随机整函数在每条水平直线上的增长性几乎必然与相应的随机Dirichlet级数的增长性相同。

The relation between coefficients and growth of a part of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane is studied. It is shown that when the random variable sequence {Xn｜ω｜} satisfies the certain condition, in the whole plane, the growth of the random integral function which is determined by the partial zero orders and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.