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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/36396
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/36396


    Title: The Factorization of Entire and Meromorphic Functions
    Authors: 洪焌維
    Jiun-Wei Hung
    Contributors: 陳天進
    Ten-Ging Chen
    洪焌維
    Jiun-Wei Hung
    Keywords: factorization of polynomial
    pseudo-prime function
    prime function
    factor
    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
    國立政治大學
    應用數學研究所
    90751002
    91
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0090751002
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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