Spring 2025 Automorphic forms and the Weil representation
The goal is to introduce the the explicit
construction of automorphic forms.
上課時間: 週一678 (13:20--14:35,
14:50:-16:15)
上課地點: 天數201
1. Motivation: Sum of squares, theta series and Eisenstein
series.
2. Local L-functions for GL(1).
3. Global L-functions for GL(1).
4. Principal series representations for GL(2) over
non-archimedean local fields.
5. Principal
series representations for GL(2) over archimedean local
fields.
6. Intertwining operators.
7. Automorphic forms on GL(2) and Eisenstein
series.
8. The Wei representation and local theta correspondence.
9. Theta series and the Siegel-Weil formula.
Reference:
Automorphic forms on GL(2), LNM 114 by Jacquet and Langlands.
Prerequisites: Complex analysis, Algebra and
Part I of GTM7