Modular Forms
We will introduce the basic concepts of modular forms and their associated L-functions, and aim at giving applications to either the Iwasawa theory or the Birch-Swinnerton-Dyer conjecture.
Lecturer
Date
24th February ~ 20th May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Tuesday | 16:10 - 17:50 | A3-2-303 | ZOOM 2 | 638 227 8222 | BIMSA |
Prerequisite
A good background on undergraduate level analysis and algebra courses is enough.
Syllabus
(1) Basis on modular forms;
(2) Eichler-Shimura isomorphisms;
(3) L-functions;
(4) Applications.
(2) Eichler-Shimura isomorphisms;
(3) L-functions;
(4) Applications.
Reference
[1] Diamond, F. and Shurman, J. A first course in modular forms. Graduate Texts in Mathematics, 228.
[2] Shimura, G. Introduction to the arithmetic theory of automorphic functions. Princeton University Press, Princeton, NJ, 1971.
[2] Shimura, G. Introduction to the arithmetic theory of automorphic functions. Princeton University Press, Princeton, NJ, 1971.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
No
Language
Chinese
, English
Lecturer Intro
Yongxiong Li, obtained a Ph.D. in Number theory from the Institute of Mathematics (CAS) . Before becoming an associate professor in BIMSA, he was an assistant professor in YMSC, Tsinghua University. His research lies in number theory, with particular interests in the arithmetic of elliptic curves, special values of L-functions and Iwasawa theory.