导数具有公共小函数的亚纯函数.pdf

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1、-43k-3"DgVol.43No.320109JournalofMathematicalStudySep.2010pz{sn12()'*+&(1.s?CZ>2Fs4
7362700;2.'3CZ!C4
7'352100)!'G!+k^$!jWAC<!+-A0(
)&x

2、oG!<!-A$wO174.52lA1
%}/TFNevanlinnar~*iX(Z[1]).S(r,f)kS(r,f)=o{T(r,f)}(r→∞

3、)*ypr*;80V7*S%
6Æ/9*HFαkT(r,f)=S(r,f)^α.f(z)*;;f(z)Yg(z).w;4F;a.f(z)Yg(z)*CM(IM)B;"a"℄Wh(Wh)e5f(z)−aYg(z)−aiVB*

4、.1TSE(f=a=g)f(z)−aYg(z)−aiV9*h*B

5、.*SSO(f=a=g)f(z)−aYg(z)−aiVB

6、.*SNE(r,a)SE(f=a=g)*WNO(r,a)SO(f=a=g)*W
;

7、.aWH11N

8、(r,)−NE(r,a)=S(r,f),N(r,)−NE(r,a)=S(r,g);f−ag−a11N(r,)−NO(r,a)=S(r,f),N(r,)−NO(r,a)=S(r,g);f−ag−a∗∗∗∗^f(z)Yg(z)CM(IM)5!a,R_a.f(z)Yg(z)*CM(IM)B;1k.baa.;Ek(a,f)f(z)−a*kh

9、.*SNk(r,f−a)1f(z)−a℄kh

10、.*WNk)(r,f−a)f(z)−a℄

11、.*hVXk(≤k)1*

12、.*WN(k(r,f−a)f(z)−a℄

13、.*hV;Xk(≥k)

14、*

15、xÆ2009-11-09310!C
f2010tq~Xk11Nk)(r,)=Ni(r,),f−af−ai=1111N(r,)=Nk)(r,)+N(k+1(r,).f−af−af−aDXF*#5!;*?V9"5*_~(pZ[2-5]),2004t℄℄#5!;*?5z[2]u1fYg.w;[Fk.;babj(j=1,2,3,4)(6≡∞)′′∗.fYg*#;9*;HfYgbj(j=1,2).CMB;∗′′bj(j=3,4).IMB;^f=g./℄&~F*k℄#*?5+G

16、Æ9bz/rA(%5_Hu2fYg.w;4*Fk.baaj(j=1,2,3,4)(6≡∞).(k)(k)∗(k)#;9*;HfYga1,a2,a3.IMB;E1(a4,f)=E(a,g(k)),E(a,f(k))⇒E(a,g(k)),(k)(k)(k)14244ÆgE2(a4,f)⇒E(a4,g),f−a4*2(k)(k)(k)h

17、.g−a4*

18、.^f=g.u3fYg.w;4*Fk,k1,k2l.baaj(j=1,2,3,4)(6≡∞)(k)(k)∗.#;9*;HfYga3,a4.IMB;(a

19、,f(k))=E(a,g(k))(i=1,2),Eki)iki)ik,k1,k2kkk1k2>k+k1+k2+2,(1)(k)(k)^f=g.2y[6]1f.4Fa1,a2,···,ap(p≥3).f*p;9*;^1ε>0,VXp1(p−2−ε)T(r,f)≤N(r,)+S(r,f).f−ajj=1[7]2Y)[/r1$=^(k)(k)S(r,f)=S(r,g):=S(r).[8]pp−13f(z).4Fp(f)=a0f+a1f+···+ap(a06=0).f*p2:Æ3aj(j=0,1,···,p)

20、l.,bj(j=0,1,···,q).q(>p);*V8^p(f)f′mr,=S(r,f).(f−b1)(f−b2)···(f−bq)-3m6,$!jWAC<!+G!3113vr#u2"(k)(k)f(z)=F(z),g(z)=G(z),^11(k)(k)N(r,F)=N(r,f)≤N(r,f)=N(r,F),22USr2p(S(r,F)=S(r,G):=S(r).R.E1(a4,F)=E1(a4,G),$V11N1(r,)=N1(r,).E2(a4,F)⇒E(a4,G),F−a4G−a4UF−a4*2h

21、.G−a4*

22、.^

23、11N2)(r,)≤N(r,).F−a4F−GR.111N(r,)=N2)(r,