Automorphic Forms

Content / Literature / Recommended previous knowledge We will interprete cuspforms for a congruence subgroup \Gamma\subset SL_2(\R) as vectors in L^2(SL_2(\R)/\Gamma). Vectors in L^2(SL_2(\R)/\Gamma) are so called automorphic forms and to certain (cuspidal) automorphic forms, such as cusp forms, one can associate an L-function satisfying a functional equation. To understand how this is done, we remember Tate's thesis, where the zeta functions were really associated to certain characters, i.e. representations of \A^*=G_m(\A). So to do "Tate's thesis for GL_2" we have to understand the representation theory of the group of adelic points GL_2(\A), where arithmetic and functional-analysis come together. Deitmar, Anton: Automorphe Formen Bump, Daniel: Automorphic forms and representations We will meet Tuesday, 2.2.2016, 10:00 c.t. in M006

Prüfungsbestandteile Vortrag, schriftliche Ausarbeitung; je nach zutreffendem Modulkatalog ist der Vortrag eine Studienleistung. Giving a presentation, writing a detailed report; depending on the applicable Modulkatalogg the presentation is a Studienleistung