Dirichlet级数与随机Dirichlet级数的迭代级数

The Iteration Series of Dirichlet Setries And Random Dirichlet Series

对于在左半平面σ <0内收敛的下侧Dirichlet级数所定义的解析函数f1(s)定义了下级 ,定义了在概率空间 (Ω ,A,P) 上的下侧随机Dirichlet级数的下级 (σ <0 ) ,研究了两类级数所定义的解析函数f1(s) ,f1(s,ω)的下级存在的条件 ;对两类由上、下侧级数迭代而成的关于无穷乘积的级数 ,讨论了它们与无穷乘积的收敛性 ,建立了它们的和函数f1[f(s) ]与f1[f(s,ω) ]在σ >

This papet has defined lower order of analytic function f 1(s) defined by lower side Dirichlet series convergence on the left half plane σ <0,and lower side random Dirichlet series( σ <0)on the probability space (Ω,A,P).It has also studied lower order existent condition of analytic Function f 1(s) and f 1(s,ω) defined by binary series,the series of infinity proauct iteration by upper and lower side Dirichlet seies,and convergence of iteration seies and infinity product.The lower order concept of f 1 and f 1 and the rilations berween this concept and the coefficients and eoponent of sum funceion f 1 and f 1 are established.