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Title: The Factorization of Entire and Meromorphic Functions
Authors: 洪焌維
Jiun-Wei Hung
Contributors: 陳天進
Ten-Ging Chen
Jiun-Wei Hung
Keywords: factorization of polynomial
pseudo-prime function
prime function
Date: 2002
Issue Date: 2009-09-18 18:28:28 (UTC+8)
Abstract: 在這篇論文中,我們將探討整函數與半純函數之分解。並且著重於質函數與擬質函數之研究。同時,我們證明某類多項式其次數為合成數且為質函數。
In this thesis, we study some factorizations of entire and
meromorphic functions, in particular, prime and pseudo-prime
functions. Also, we obtain a new class of prime polynomials of
composite degree.
Abstract i
中文摘要 ii
1 Introduction 1
2 Factorization of Polynomials 2
3 Pseudo-prime Functions 20
4 Prime Functions 27
5 An application 40
References 47
Reference: [1] I. N. Baker and F. Gross, Further Results on Factorization
of Entire Functions, Proc. Sympos. in Pure Math. 11, Entire
Functions and Related Parts of Analysis, 30 (1968).
[2] A. Edrei and W. H. Fuchs, On the zeros of
f(g(z)) where f and g are entire functions}, J. Analyse
Math.12, 243-255 (1964).
[3] F. Gross, On the Periodicity of Compositions of Entire
Functions, Canadian J. Math. 18, 724 (1966).
[4] F. Gross, On Factorization of Meromorphic Functions, Trans.
Amer. Math. Soc. 131, 215 (1968).
[5] F. Gross, Factorization of Entire Functions which are
Periodic Mod g, Indian J. Pure Appl. Math. 2, No. 3 (1971).
[6] F. Gross, Factorization of Meromorphic Functions, U.S.
Government Printing Office, Washington, D.C. (1972).
[7] F. Gross, Factorization of Meromorphic Functions and Some
Open Problems, Lecture Notes in Math, vol. 599 (1977).
[8] W. K. Hayman, Meromorphic Functions, Oxford Mathematical
Monographs, Clarendon Press, Oxford, 1964.
[9] W. K. Nicholson, Introduction to Abstract Algebra, John
Wiley and Sons, New York, 1999.
[10] R. Nevanlinna, Le the'ore'me de Picard-Borel et la
the'orie des fonctions me'romorphes, Gauthier-
Villar, Paris,1929.
[11] G. Po'lya, On An Integral Function of An Integral
Function, J. London Math. Soc. 1, 12 (1926).
[12] J. F. Ritt, Prime and Composite Polynomials, Trans. Amer.
Math. Soc. 23, 51 (1922).
[13] P. C. Rosenbloom, The Fix-points of Entire Functions, Medd
Lunds. Univ. Mat-Sum. Suppl. Ed. M. Riesz, 186-192 (1952)
Description: 碩士
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Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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