The course will introduce automorphic forms on GL_2(A_Q). We will first introduce adeles A_Q over the rational numbers Q and Fourier analysis on it. Then we will introduce the automorphic forms on GL_1(A_Q) (the ideles over Q), which is a generalisation of Dirichlet characters. After that we will move to GL_2(A_Q). We will generalise the notion of modular forms to automorphic functions and study Maass forms and their Fourier expansions. Hecke operators will then be defined in an adelic way. Then we will introduce automorphic forms on GL_2(A_Q) and automorphic representations of GL_2(A_Q).
Prerequisites: the course Modular Forms-1 (chapters 1-5 of Diamond-Shurman, A first course in modular forms; in particular the definitions of modular forms and Hecke operators).
- verantwortliche Lehrperson: Gautier Jean Christian Ponsinet
- verantwortliche Lehrperson: Xiaoyu Zhang