右半平面上随机Dirichlet级数的增长性

The growth of random Dirichlet series in the right half plane

研究右半平面上无限级随机Dirichlet级数的增长性.利用型函数证明了:若随机Dirichlet级数f(s,ω)=∑∞n=1anXn(ω)exp(-λns)(s=σ+it),满足limn→∞ln|an|λn=0,nl→im∞lλnnn=0,且随机变量{Xn(ω)}满足sn≥up1{E|Xn|α}<+∞,snu≥1p{E|Xn|-β}<+∞,则limσ→0+ln+ln+M(σ,ω)lnU(1/σ)=1 n l→im+∞tn=1,得到了关于无限级随机Dirichlet级数增长性的一个充要条件.

The right half plane infinite growth of random Dirichlet series is studied. By using type function, it is proved that if random Dirichlet series f so a necessary and sufficient condition is obtained.