右半平面无限级随机Dirichlet级数值的分布  

The Distribution of Values of the Infinite Order Random Dirichlet Series on the Right Half-Plane

作　　者：王志刚[1] 田范基[2] 

机构地区：[1]海南大学数学系 [2]湖北大学数学与统计学学院

出　　处：《数学物理学报（A辑）》2015年第2期245-255,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11261015);海南省自然科学基金(20151002)资助

摘　　要：该文主要研究了右半平面无限级随机Dirichlet级数值的分布.首先,在较宽的系数条件下证明了右半平面随机Dirichlet级数增长性和值的分布定理.其次,研究了系数的模为两两NQD列的随机Dirichlet级数的性质,得到与独立随机序列类似的结果.在一定的条件下,右半平面上随机级数Σ∞n=0X_ne^(-λ_ns)与级数Σ∞n=0σ_ne^(-λ_ns)a.s.有相同的收敛横坐标、增长级和型函数.The emphasis in this paper is mainly on the distribution of values of the infinite order random Dirichlet series on the right half-plane. Firstly, the theorem of the growth and the distribution of value of the Dirichlet series on the right half-plane are proved under some weak conditions of the coefficient. Secondly, the random Dirichlet series the norms of whose coefficients are pairwise NQD sequences are investigated and some better results similar to the case of independent random sequences are obtained. Under some conditions, the random series n=0Σ^∞Xne^-λns and the series n=0Σ^∞σne^-λns a.s. have the same abscissa of convergence, the order of growth, the type function on the right half-plane.

关 键 词：随机DIRICHLET级数 增长性 值的分布 两两NQD序列 型函数 

分 类 号：O211.5[理学—概率论与数理统计]