This course aims to introduce automorphic forms and automorphic representations for GL_2(A_Q). We shall first introduce the adelic ring and the Fourier analysis of them. We will then talk about automorphic forms and automorphic representations for GL_1(A_Q). In particular, we shall explain Tate's thesis on the L-functions of Hecke characters. After that, we shall study automorphic forms on GL_2(A_Q), we will talk about Maass forms, Whittaker functions, Maass raising/lowering operators, Eisenstein series, etc. In the end, we will discuss automorphic representations for GL_2(A_Q).
Prerequisites: Complex analysis, Modular form 1 (basic definitions, Hecke operators, L-functions). Basic results from Modular Forms 1 can be recalled quickly upon request (in particular, we also welcome students who have not followed Modular Forms 1).
Main Reference: 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