PRECISE FUNDAMENTAL INEQUALITIES AND SUM OF DEFICIENCIES  

作　　者：杨乐 

机构地区：[1]Institute of Mathematics, Academia Sinica, Beijing 100080, PRC

出　　处：《Science China Mathematics》1991年第2期157-165,共9页中国科学：数学（英文版）

基　　金：Project partially supported by the National Natural Science Foundation of China.

摘　　要：In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f(z) be transcendental mero-morphic in the finite plane and k be a positive integer. If ε is an arbitrary positive numberand a and b are two distinct finite complex numbers, then we have T(r,f)<(1+1/k)N (r,1/f)+(1+1/k)N (r,1/(f^(k)-1)) -N (r,1/(f(k+1))+εT(r,f)+S(r,f)and δ(a,f^(k))+δ(b,f^(k))≤1+1/(2k+1).In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f（z） be transcendental mero-morphic in the finite plane and k be a positive integer. If ε is an arbitrary positive numberand a and b are two distinct finite complex numbers, then we have T（r,f）&lt;（1+1/k）N （r,1/f）+（1+1/k）N (r,1/(f^k-1)) -N (r,1/（f（k+1））+εT（r,f）+S（r,f）and δ(a,f^k)+δ(b,f^k)≤1+1/（2k+1）.

关 键 词：DEFICIENCY PRECISE Hayman INEQUALITY fundamental. 

分 类 号：N[自然科学总论]