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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 8-Dec-2010 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
dc.contributor.advisor 陳天進zh_TW
dc.contributor.author (Authors) 陳薇zh_TW
dc.contributor.author (Authors) Chen, Weien_US
dc.creator (作者) 陳薇zh_TW
dc.creator (作者) Chen, Weien_US
dc.date (日期) 2008en_US
dc.date.accessioned 8-Dec-2010 11:48:34 (UTC+8)-
dc.date.available 8-Dec-2010 11:48:34 (UTC+8)-
dc.date.issued (上傳時間) 8-Dec-2010 11:48:34 (UTC+8)-
dc.identifier (Other Identifiers) G0095751014en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49454-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 95751014zh_TW
dc.description (描述) 97zh_TW
dc.description.abstract (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.zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents 謝辭-------------------------------------------------------i
Abstract-------------------------------------------------iii
中文摘要---------------------------------------------------iv
1 Introduction---------------------------------------------1
2 General Theory of Valuations-----------------------------2
3 Topology of Valuated Fields-----------------------------16
4 Completion of Valuations--------------------------------24
5 Equivalence of Valuations-------------------------------34
6 p-Adic Number Field and Arithmetic----------------------43
7 p-Adic Series-------------------------------------------52
References------------------------------------------------59		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0095751014en_US
dc.subject (關鍵詞) p進位數zh_TW
dc.subject (關鍵詞) 賦zh_TW
dc.subject (關鍵詞) p-adicen_US
dc.subject (關鍵詞) valuationen_US
dc.subject (關鍵詞) valuated fielden_US
dc.title (題名) 探討p進位數之分析zh_TW
dc.title (題名) On some p-adic analysisen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Referenceszh_TW
dc.relation.reference (參考文獻) [1]T. M. Apostol, Mathematical Analysis, Addion-Wesley, 1974.zh_TW
dc.relation.reference (參考文獻) [2]G. Bachman, Introduction to p-Adic Numbers and Valuation Theory, Academic Press, New York and London, 1964.zh_TW
dc.relation.reference (參考文獻) [3]J. W. S. Cassels, Local Fields, Cambridge University Press, Cambridge, 1986.zh_TW
dc.relation.reference (參考文獻) [4]J. B. Fraleigh, A First Course in Abstract Algebra, 7thzh_TW
dc.relation.reference (參考文獻) Ed., Addion-Wesley, 2003.zh_TW
dc.relation.reference (參考文獻) [5]I. N. Herstein, Topics in Algebra, New York: Blaisdell,zh_TW
dc.relation.reference (參考文獻) 1964.zh_TW
dc.relation.reference (參考文獻) [6]S. Katok, Real and $p$-Adic Analysis Course Notes, http://www.math.psu.edu/katok_s/pub/p-adic.pdf, 2001.zh_TW
dc.relation.reference (參考文獻) [7]N. Koblitz, p-Adic Numbers, p-Adic Analysis, and Zeta-Functions, Springer-Verlag, Berlin, Heidelberg, New York,zh_TW
dc.relation.reference (參考文獻) 2nd Ed., 1984.zh_TW
dc.relation.reference (參考文獻) [8]K. Mahler, p-Adic Numbers and Their Functions, Cambridgezh_TW
dc.relation.reference (參考文獻) Press, 1973.zh_TW
dc.relation.reference (參考文獻) [9]A. M. Robert, A Course in p-Adic Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 2000.zh_TW
dc.relation.reference (參考文獻) [10]W. H. Schikoff, Ultrametric Calculus, An Introduction tozh_TW
dc.relation.reference (參考文獻) p-Adic Analysis, Cambridge Studies in Adv. Math.4, Cambridgezh_TW
dc.relation.reference (參考文獻) University Press, 1984.zh_TW