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

作　　者：杨祺[1] 田宏根[1] 

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830054

出　　处：《数学杂志》2011年第6期1079-1086,共8页Journal of Mathematics

基　　金：新疆师范大学优秀青年教师科研启动基金资助(XJNU0816);国家自然科学基金资助课题(10471048)

摘　　要：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.

关 键 词：DIRICHLET级数 随机DIRICHLET级数 型函数 下级 

分 类 号：O174.52[理学—数学]