关于一般微分单项式的值分布(英文)

ON VALUE DISTRIBUTIONS OF GENERAL DIFFERENTIAL MONOMIALS

讨论了一般微分单项式的值分布 ,得到定理 :设 f 是平面上的超越亚纯函数 .F=fn0 (f( i) ) ni… (f( k) ) nk-c,ni≥ 1,c≠ 0是常数 ,那么 (n0 -2 ) T(r,f )≤ N(r,1F ) + S(r,f ) n0 >2T(r,f )≤ 7(i+ 1)i (Ni) (r,1f ) + N(r,1F) ) + S(r,f ) n0 =1T(r,f )≤ 7(N (r,1f ) + N(r,1F) ) + S(r,f ) n0 =0 .

Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) n k -c,n i≥1,c≠0 be a constant then (n 0-2)T(r,f)≤(r,1F)+S(r,f) when n 0>2;T(r,f)≤7(i+1)i( i) (r,1f)+(r,1F))+S(r,f) when n 0=1;T(r,f)≤7(N(r,1f)+(r,1F))+S(r,f) when n 0=0.