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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
L-functions
Spring 2024, Jinan
Time and Place:
Tuesday 14:00-16:00, 逸夫信息楼 A403.
Instructors:
Bingrong Huang and Yongxiao Lin
Prerequisites:
Basic Analytic Number Theory and Automorphic Forms.
Syllabus:
This is a reading course. We plan to read the following chapters and papers in this semester.
[BFKMMS] Blomer, Valentin; Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe; Milićević, Djordje; Sawin, Will. The second moment theory of families of L-functions—the case of twisted Hecke L-functions. Mem. Amer. Math. Soc. 282 (2023), no. 1394, v+148 pp. MR4539366
[FKMS] Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe; Sawin, Will. Lectures on applied ℓ-adic cohomology. Analytic methods in arithmetic geometry, 113–195, Contemp. Math., 740, Centre Rech. Math. Proc., Amer. Math. Soc., [Providence], RI, [2019], ©2019. MR4033731
[BFKMM] Blomer, Valentin; Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe; Milićević, Djordje. On moments of twisted L-functions. Amer. J. Math. 139 (2017), no. 3, 707–768.
[BFKMM] Blomer, V.; Fuvri, É.; Kovalʹski, È.; Mishelʹ, F.; Milichevich, Dzh. Some applications of smooth bilinear forms with Kloosterman sums. (Russian) English version published in Proc. Steklov Inst. Math. 296 (2017), no. 1, 18–29. Tr. Mat. Inst. Steklova 296 (2017), Analiticheskaya i Kombinatornaya Teoriya Chisel, 24–35.
Schedule:
| Date | Speaker | Title | References |
| February 27 | Yongxiao Lin | Momemts of L-functions | [BFKMMS] Chap. 1 |
| March 05 | Yongxiao Lin | Momemts of L-functions, II | [BFKMMS] Chap. 1 |
| March 12 | Chenyang Lu |
L-functions |
[BFKMMS] Chap. 2 |
| March 19 | Chenyang Lu |
L-functions, II |
[BFKMMS] Chap. 2 |
| March 26 | Bin Guan | Local Langlands conjecture | |
| April 02 | Liangxun Li | The twisted moments |
[BFKMMS] Chap. 4 |
| April 09 | Liangxun Li | The twisted moments, II |
[BFKMMS] Chap. 5 |
| April 16 | Liangxun Li | The +ab shift |
[FKMS] Sec. 16 |
| April 23 | Zhehao He |
Non-vanishing | [BFKMMS] Chap. 6 |
| April 30 | Zhehao He |
Non-vanishing, II | [BFKMMS] Chap. 6 |
| May 07 | Jiangpeng Li | Extreme values | [BFKMMS] Chap. 7 |
| May 14 | Jiangpeng Li | Extreme values, II | [BFKMMS] Chap. 7 |
| May 21 | Jinghai Liu | The analytic rank | [BFKMMS] Chap. 8 |
| May 28 | Haozhe Gou | Algebraic exponential sums | [BFKMMS] Chap. 3 |
| June 04 | Haozhe Gou | Algebraic exponential sums | [BFKMMS] Chap. 3 |
| June 11 | Zhenyu Zhang | Modular symbols | [BFKMMS] Chap. 9 |
| June 18 | Bingrong Huang | Fourth moment of GL(1) L-functions | [BFKMM] |
Contact:
Bingrong Huang (Email: brhuang (AT) sdu.edu.cn; Office: Mingde Building C701)
Yongxiao Lin (Email: yongxiao.lin (AT) sdu.edu.cn; Office: Mingde Building C705)