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THE SUM OF DEFICIENCIES OF ENTIRE FUNCTION ON Cⁿ

Department of Mathematics, Fudan Unviersity, Shanghai 200433, China

and

Department of Basic Courses, University of Shanghai for Science and Technology, Shanghai 200093, China

Abstract

This paper proves that: Let f be an entire function of finite order λ on Cⁿ. Then

(1) , where k(λ) is a nonnegative constant depending only on λ;

(2) If , then λ is a positive integer and equals the lower order of f.

Project supported by the National Natural Science Foundation of China (No.10271029).

Document Code: A, Article ID: 0252-9599(2003)02-0221-06

Keywords:

D. Drasin and A. Weitsman, Advances in Math. 15, 93 (1974), DOI: 10.1016/0001-8708(75)90126-7. Crossref, Google Scholar
S. Mori, Nagoya Math. J. 67, 165 (1977). Crossref, Google Scholar
S. Mori, Tôhoku Math. J. 31, 285 (1979), DOI: 10.2748/tmj/1178229796. Crossref, Google Scholar
R. Nevanlinna , Analytic functions ( Springer-Verlag , New York , 1970 ) . Crossref, Google Scholar
J. Noguchi, Nagoya Math. J. 59, 97 (1975). Crossref, Google Scholar
A. Pfluger, Comment. Math. Helv. 19, 91 (1946), DOI: 10.1007/BF02565950. Crossref, Google Scholar
M. Ru , Nevanlinna theory and its relation to Diophantine approximation ( World Scientific Publishing Co. , Singapore , 2001 ) . Link, Google Scholar
B. V. Shabat , Distribution of values of holomorphic mappings , Translations of Mathematical Monographs 61 ( Amer. Math. Soc. , 1985 ) . Crossref, Google Scholar
L. Yang , Value distribution theory ( Springer-Verlag , Berlin-Heidelberg , 1993 ) . Google Scholar
Z. Ye, Math. Z. 222, 81 (1996), DOI: 10.1007/BF02621859. Crossref, Google Scholar