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    題名: 探討p進位數之分析
    On some p-adic analysis
    作者: 陳薇
    Chen, Wei
    貢獻者: 陳天進
    陳薇
    Chen, Wei
    關鍵詞: p進位數
    賦
    p-adic
    valuation
    valuated field
    日期: 2008
    上傳時間: 2010-12-08 11:48:34 (UTC+8)
    摘要: 在這篇論文裡, 我們探討體中之賦值的一般理論. 最主要的, 我們證明了多個賦值等價條件. 進而我們探討p進位數體中的分析, 得到ㄧ些新的現象與例子.
    In this thesis, we study some general theory of valuations on a field. Especially, we obtain several equivalent conditions on the equivalence of two valuations on a field, some of them are new in the literature. Moreover, we study the $p$-adic analysis on the p-adic number fields and obtain some new phenomena and examples.
    參考文獻: References
    [1]T. M. Apostol, Mathematical Analysis, Addion-Wesley, 1974.
    [2]G. Bachman, Introduction to p-Adic Numbers and Valuation Theory, Academic Press, New York and London, 1964.
    [3]J. W. S. Cassels, Local Fields, Cambridge University Press, Cambridge, 1986.
    [4]J. B. Fraleigh, A First Course in Abstract Algebra, 7th
    Ed., Addion-Wesley, 2003.
    [5]I. N. Herstein, Topics in Algebra, New York: Blaisdell,
    1964.
    [6]S. Katok, Real and $p$-Adic Analysis Course Notes, http://www.math.psu.edu/katok_s/pub/p-adic.pdf, 2001.
    [7]N. Koblitz, p-Adic Numbers, p-Adic Analysis, and Zeta-Functions, Springer-Verlag, Berlin, Heidelberg, New York,
    2nd Ed., 1984.
    [8]K. Mahler, p-Adic Numbers and Their Functions, Cambridge
    Press, 1973.
    [9]A. M. Robert, A Course in p-Adic Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 2000.
    [10]W. H. Schikoff, Ultrametric Calculus, An Introduction to
    p-Adic Analysis, Cambridge Studies in Adv. Math.4, Cambridge
    University Press, 1984.
    描述: 碩士
    國立政治大學
    應用數學研究所
    95751014
    97
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0095751014
    資料類型: thesis
    顯示於類別:[應用數學系] 學位論文

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