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題名: | The Factorization of Entire and Meromorphic Functions | 作者: | 洪焌維 Jiun-Wei Hung |
貢獻者: | 陳天進 Ten-Ging Chen 洪焌維 Jiun-Wei Hung |
關鍵詞: | factorization of polynomial pseudo-prime function prime function factor |
日期: | 2002 | 上傳時間: | 18-Sep-2009 | 摘要: | 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\r\nmeromorphic functions, in particular, prime and pseudo-prime\r\nfunctions. Also, we obtain a new class of prime polynomials of\r\ncomposite degree. Abstract i\r\n中文摘要 ii\r\n1 Introduction 1\r\n2 Factorization of Polynomials 2\r\n3 Pseudo-prime Functions 20\r\n4 Prime Functions 27\r\n5 An application 40\r\nReferences 47 |
參考文獻: | [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) |
描述: | 碩士 國立政治大學 應用數學研究所 90751002 91 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0090751002 | 資料類型: | thesis |
Appears in Collections: | 學位論文 |
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