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課程名稱 |
基礎解析數論
Introduction to Analytic Number Theory |
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開課學期 |
107-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
郭文堂 |
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課號 |
MATH5094 |
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課程識別碼 |
221 U8390 |
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班次 |
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學分 |
3.0 |
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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 |
星期二2,3(9:10~11:10)星期三2(9:10~10:00) |
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上課地點 |
天數304天數304 |
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備註 |
與劉育如合授
限學士班三年級 或 限碩士班以上
總人數上限：15人 |
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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 |
The goal of this course is to introduce to students some basic tools in analytic number theory. The following topics will be covered in the course:
1. Prime Numbers
2. Mobius function, von Mangold function, Abel’s summation
3. Riemann’s zeta function and prime number theorem
4. ω and Ω functions
5. Quadratic Reciprocity
6. Primitive Roots
7. Characters, L-functions and Dirichlet’s
8. Circle Method and its Applications
9. Sieve Methods and their Applications |
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課程目標 |
The goal of this course is to introduce to students some basic tools in analytic number theory, such as Abel’s summation, L-functions, the circle method and sieve methods. The targeted audiences are upper-year undergraduate students and graduate students in their early study. |
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課程要求 |
Basic Knowledge in 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 |
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參考書目 |
There is no required textbook for the course. The following books are good references:
1. Introduction to Analytic Number Theory (by T. Apostol; Springer)
2. Multiplicative Number Theory (by H. Davenport; Springer)
3. The Hardy-Littlewood Method (by R. Vaughan; Cambrige)
4. Sieve methods and their Applications (by A. Cojocaru and R. Murty, Springer)
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評量方式
(僅供參考) |
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