摘要
本文研究B-Dirichlet级数的增长性态。证明在很一般的条件下,它和一个对应的Dirichlet级数具有相同的(p,q)级(R)及(p,q)下级(R)。文中还讨论了B-Dirichlet级数的正则增长性问题,它推广了余家荣关于Dirichlet级数的相应结果。
Let ψ_τ_0 be an entire f(?)nction defined by a B-Dirichletian element {ψ_τ_0}: (?)P_n(σ+i_τ_0) exp (-λ_ns), where s=σ+iτ, τ_0 is an arbitrary fixed real unmber, λ_n is a sequence of strictly increasing positive numbers tending to infinity with n and P_n(s)=(?) a_(nj)s^j(n=1, 2, …), are complex polynomials. We associate., it with a Dirichlet series ψ(s)= (?)A_nexp(-λ_ns). where A_n=(?). It is shown in this paper that the (p, q) order (R) or lower order of ψ_τ_0 is eaqual to that of ψ whenever σ(?)=-∞, β'=(?) sup((m_n)/(λ_n))<∞ and L=limsup ((logn)/(λ_n))<∞, where (?) denotes the abscissa of convergence of ψ and p≥q+2. A necessary and sufficient condition under which ψ_τ_0 is of regular growth is also given
出处
《武汉大学学报（自然科学版）》
CSCD
1989年第4期1-7,共7页
Journal of Wuhan University(Natural Science Edition)
基金
国家自然科学基金
关键词
B-Dirichlet
DIRICHLET
级数
B-Dirichlet series
Dirichlet series
Ritt-order(lower order)
(p. q)-order(lower order)
