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Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/49454


Title: 探討p進位數之分析
On some p-adic analysis
Authors: 陳薇
Chen, Wei
Contributors: 陳天進
陳薇
Chen, Wei
Keywords: p進位數

p-adic
valuation
valuated field
Date: 2008
Issue Date: 2010-12-08 11:48:34 (UTC+8)
Abstract: 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.
Reference: 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.
Description: 碩士
國立政治大學
應用數學研究所
95751014
97
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0095751014
Data Type: thesis
Appears in Collections:[Department of Mathematical Sciences] Theses

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