右半平面上指数级Dirichlet级数

摘要

By the method of Knopp-Kojima, the growths of the Dirichlet series of the exponential order in the right half plane are studied. The results of the connection between the coefficients of the Dirichlet series and the exponential order growth are obtained. (i) If a zero order series over σ 〉 0 has exponential order μ, then —lim σ→0+ ln+-Mu(σ)/(ln1/σ)ν=μv= —lim n→+∞ ln+-Ank/(lnnk)v where nk is the main index sequence, 0 〈μv 〈+ ∞,v＞1；(ii) If σu=0 and a zero order series over σ〉 0 has exponential order τ, then lim/σ→0+ln+-Mu(σ)/(ln 1/σ)v=τv=lim→+∞ ln+-Acn/(lnn)v,where 0 〈μv〈 + ∞, v 〉 1.%用Knopp-Kojima方法研究右半平面上指数级Dirichlet级数的增长性,得到系数与指数级增长性关系的结果:(i)对σ＞0上零级级数有指数级μv,则(limσ→0+)(ln+-Mu(σ))/(0+(ln1/σ)ν)=μv=(limn→+∞)(ln+-An)/((lnn)v)=(limn→+∞)(ln+Ank)/((lnnk)v),其中nk为主要指标序列,0＜μv＜+∞,v＞1；(ii)对σ＞0上零级级数,若σu=0且有指数下级τv,则(lim+σ→0+)(ln+Mu(σ))/(ln(1/σ)=τv=(limn→+∞)(ln+Anc)/((lnn)v),其中0＜μv＜+∞,v＞1.