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个人信息Personal Information
教授 博士生导师 硕士生导师
性别：男
毕业院校：山东大学
学历：研究生(博士)毕业
学位：理学博士学位
在职信息：在职
所在单位：数据科学研究院
入职时间：2019-08-30
学科：基础数学
办公地点：明德楼C701
联系方式：(0531) 883 69786
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Automorphic forms
Fall 2022, Jinan
Time and Place:
Thursday 09:00-12:00, Zhixin Building B1044.
Prerequisites:
Basic Analytic Number Theory and Modular Forms.
Syllabus:
We plan to give lectures on automorphic forms in this semester. We will use the following book:
Iwaniec, Henryk. Spectral methods of automorphic forms. Second edition. Graduate Studies in Mathematics, 53. American Mathematical Society, Providence, RI; Revista Matemática Iberoamericana, Madrid, 2002. xii+220 pp.
Schedule:
| Week | Date | Contents |
| 1 | Sep. 08 |
No class |
| 2 | Sep. 15 | Introduction; The upper half plane and Group decompositions |
| 3 | Sep. 22 | The Laplace operator and eigenfunctions |
| 4 | Sep. 29 | The invariant integral operators and Green functions |
| 5 | Oct. 06 | Fuchsian groups |
| 6 | Oct. 13 | Kloosterman sums |
| 7 |
Oct. 20 | Automorphic forms |
| 8 | Oct. 27 | The spectral theorem of discrete part |
| 9 | Nov. 03 | The automorphic Green function |
| 10 | Nov. 10 | Analytic continuation of the Eisenstein series |
| 11 | Nov. 17 | The spectral theorem of continuous part |
| 12 | Nov. 24 | Averages of Fourier coefficients |
| 13 | Dec. 01 | Kuznetsov trace formula |
| 14 | Dec. 08 | Selberg trace formula |
| 15 | Dec. 15 | Selberg trace formula, II |
| 16 | Dec. 22 | Weyl's law |
Contact: Bingrong Huang (Email: brhuang@sdu.edu.cn; Office: Mingde Building C701)
Course homepage: https://faculty.sdu.edu.cn/brhuang/zh_CN/zdylm/1477561/list/index.htm