摘要
本文主要证明了下述定理: 设f(z)=sum from n=0 to∞a_nz^(λ_n)为一超越整函数,那么: (1)当f(z)具有(b,d)型A.P.间隙时,对任一有穷复数a,都有δ_s(a,f)≤1-1/d;当b>0时,还有:sum from a≠∞ to δ(a,f)≤1-1/d。 (2):当λ_(m+1)-λ_m(m=n,n+1,…)的最大公因子d_n→∞(n→∞)时,对在一慢增长的亚纯函数a(z),都有:_s(a(z),f)≤1/2。
Suppose that f(z)=sum form n=0 to ∞ is a transcendental entire function, if f(z) has A. P. gaps of (b, d) type, then ο_s(a, f)≤1-(1/d) for every finite a.In particular if b>0 then sum from a≠∞ δ(a, f)≤1-(1/d). Also let d_n be the highest common factor of all the numhers λ_(m+1)-λ_m for m≥n and suppose that d_n→∞(n→∞), then _s(a(z), f)≤(1/2) for every meromorphic funoction growing slowly compared with the function f(z).
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
1989年第1期25-32,共8页
Journal of East China Normal University(Natural Science)
关键词
b
d型
A
P
间隙
模分布
A. P. gaps transcendental entire function modula distribution
