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https://ah.lib.nccu.edu.tw/handle/140.119/49454| 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: | 8-十二月-2010 | 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 |
| Appears in Collections: | 學位論文 |
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| File | Description | Size | Format | |
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| 101401.pdf | 130.83 kB | Adobe PDF2 | View/Open | |
| 101402.pdf | 220.39 kB | Adobe PDF2 | View/Open | |
| 101403.pdf | 332.43 kB | Adobe PDF2 | View/Open | |
| 101404.pdf | 349.64 kB | Adobe PDF2 | View/Open | |
| 101405.pdf | 111.33 kB | Adobe PDF2 | View/Open | |
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| 101410.pdf | 182.38 kB | Adobe PDF2 | View/Open | |
| 101411.pdf | 180.43 kB | Adobe PDF2 | View/Open | |
| 101412.pdf | 113.3 kB | Adobe PDF2 | View/Open |
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