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課程名稱 |
代數數論
Algebraic Number Theory |
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開課學期 |
103-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
于 靖 |
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課號 |
MATH5170 |
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課程識別碼 |
221 U6360 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一7(14:20~15:10)星期三1,2(8:10~10:00) |
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上課地點 |
天數304天數304 |
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備註 |
總人數上限：15人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1031MATH5170_ANT |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
We study the arithmetic of number fields. Will start with a direct global approach, ideal-lattice theoretic. Then local-global approach via addles-ideles. After introducing all the basic invariants of a number field, we study L-functions, and zeta functions. Special families of number fields will be brought to stage from time to time as examples. Class field theory will be connected with the main line throughout the major development. |
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課程目標 |
Algebraic number theory, including class field theory. Will use all kind of tools.
Analytic part of the theory, including the explicit formula following Weil.
Computational aspects, up to computational class field theory.
Special values of L-functions, and its roles.
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課程要求 |
Elementary number theory, introductory algebra, introductory analysis, linear algebra, basic complex analysis. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
1. Any book on elementary number theory, in particular, quadratic reciprocity.
2. M. Artin, Algebra, Chap.13, quadratic number fields, 2nd ed. Prentice-Hall, 2011
3. J.-P. Serre, A course in arithmetic, GTM, Springer Verlag 1996. |
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參考書目 |
1. Z. I. Borevich & I. R. Shafarevich, Number Theory, Academic Press 1986.
2. J. W. S. Cassels & A. Frohlich, Algebraic Number Theory 2010.
3. H. Cohen, A course in computational algebraic number theory, GTM, Springer 2000.
4. A. Frohlich & M. Taylor, Algebraic Number Theory, Cambridge U. Press, 1993.
5. E. Hecke, Lectures on the theory of Algebraic Numbers, GTM, Springer Verlag 2010.
6. S. Lang, Algebraic Number Theory, GTM, Springer Verlag 2001.
7. J. Neukirch, Algebraic Number Theory, a series of comprehensive studies, SpringerVerlag 1999.
8. J.-P. Serre, Local Fields, GTM, Springer Verlag 1995.
9. H. P. F. Swinnerton-Dyer, A brief guide to Algebraic Number Theory, Cambridge U. Press, 2001.
10. A. Weil, Basic Number Theory, Classics in Math 2013, Springer Verlag.
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評量方式
(僅供參考) |
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