The lectures and exercise sessions of this course will take place at WSC-S-U-3.02 with video-streaming by Zoom at the same time.
Lectures: Monday 10h-12h, Wednesday 10h-12h; Exercise sessions (by Dr. Xiaoyu Zhang): Friday 16h-18h.
The course aims to introduce the basic theory of modular forms and related topics. We will talk about the definition of modular forms, their q-expansions, Hecke operators, L-functions, modular curves, and some interesting applications. If time permits, we shall talk about some advanced topics, in the end, depending on the interests of the students. Basic knowledge of complex analysis is requested.
References:
[1] F. Diamond and J. Shurman, A first course in modular forms, GTM 228, Springer, 2005.
[2] D. Bump, Automorphic forms and representations, CSAM 55, Cambridge University Press, 1997.
[3] N. Koblitz, Introduction to elliptic curves and modular forms, GTM 97, Springer, 1984.
[4] D. Goldfeld and J. Hundley, Automorphic Representations and L-functions for the General Linear Group, CSAM 129, Cambridge University Press, 2011.
- Lehrende(r): Jie Lin
- Lehrende(r): Xiaoyu Zhang