課程名稱 |
GL(2)上的自守形式 Automorphic forms on GL(2) |
開課學期 |
110-1 |
授課對象 |
理學院 數學系 |
授課教師 |
謝銘倫 |
課號 |
MATH5267 |
課程識別碼 |
221 U9130 |
班次 |
|
學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期五6,7,8(13:20~16:20) |
上課地點 |
天數201 |
備註 |
總人數上限:10人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1101MATH5267_ |
課程簡介影片 |
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
課程概述 |
(I) Local theory of representation on GL(2)
(1) Weil representations on SL(2)
(2) Explicit construction of representations on GL(2) as quotients of Weil representations
(3) Construction of Whittaker models and Kirillov models
(4) Classification of admissibl
e irreducible representations on GL(2)
(II) Eisenstein series on GL(2) and applications
(1) Intertwining operators
(2) Explicit computation of Fourier coefficients and constant terms
(3) Non-vanishing of the Riemann zeta function at 1+it, t\not =0
(4) Langlands' computation of Tamagawa number of SL(2)
(III) Theta liftng
(1) Local Jacquet-Langlands correspondence
(2) Jacquet-Langlands-Shimizu lift
(IV) Theory of L-functions
(1) L-functions for GL(2) and converse theroems
(2) L-functions for GL(2)xGL(2): Rankin-Selberg convolution
(3) Quadratic base change |
課程目標 |
This an introductory course for automorphic representations and associated L-functions on GL(2). |
課程要求 |
Complex analysis and linear algebra |
預期每週課後學習時數 |
|
Office Hours |
|
指定閱讀 |
待補 |
參考書目 |
Jacquet-Langlands. Automorphic forms on GL(2), part I, LNM 114.
Jacquet. Automorhic forms on GL(2), part II, LNM 278.
Shimizu, Hideo. Theta series and automorphic forms on GL(2), J. Math. Soc. Japan, vol 24 p.638-683. |
評量方式 (僅供參考) |
|
|