整Dirichlet级数的一些性质

Some Properties of Entire Dirichlet Series

证明了Dirichlet级数g(s)=sum from n=1 to ∞ anbne-λns,h(s)=sum from n=1 to ∞ anb-n1e-λns和f(s)=sum from n=1 to ∞ ane-λns(s=σ+it)在一定条件下有相同的级、下级、型和(p,q)(R)-级及下(p,q)(R)-级。

It proved the Dirichlet series sum from n=1 to ∞ anbne-λns,h(s)=sum from n=1 to ∞ anbn-1e-λnsandf(s)=sum from n=1 to ∞ ane-λns(s=σ+it)whichhavethesame order,the same lower order,the same type and the same(p,q)(R)-order,the same lower(p,q)(R)-order in some condition.