Dirichlet级数和随机Dirichlet级数的下级增长性

GROWTH OF THE LOWER ORDER OF DIRICHLET SERIES AND RANDOM DIRICHLET SERIES

本文研究了全平面上零级和有限级Dirichlet级数及随机Dirichlet级数的下级增长性.利用型函数,得到了其系数和增长性之间的关系,以及当随机变量序列{X_n(ω)}满足一定条件时,零级和有限级随机Dirichlet级数在全平面上所确定的随机整函数在每条水平直线上的下级增长性几乎必然与相应的随机Dirichlet级数的下级增长性相同.

The growth of the lower order of zero order and finite order Dirichlet series and random Dirichlet series are studied in the whole plane. By using type-function, a relation between coefficients and growth of the Dirichlet series is obtained. And also, when the random variable sequence {Xn（ω）} meets certain condition in the whole plane, the growth of the lower order of the random entire function determined by zero orders and finite order random Dirichlet series is almost surely the same as the corresponding growth of the lower order of random Dirichlet series on any horizontal straight line.