March 17 - May 6, 2010
Lectures: Wednesday & Thursday: 09:00 - 11:00
Seminar: Thursday: 16:00 - 17:00
ESI, Schrödinger lecture hall

 
Abstract:
Eisenstein series play an important role in the spectral decomposition of the space of square-integrable automorphic forms on the adelic points of a reductive algebraic group defined over a number field. In particular, the continuous part of the spectrum can be described using direct integrals of Eisenstein series, while the non-cuspidal part of the discrete spectrum is spanned by certain residues of Eisenstein series. Their importance goes beyond square-integrability in view of the fact that the space of all automorphic forms can be described using the residues and principal values of the derivatives of Eisenstein series. This course is ment to be an introductory course to Eisenstein series at the graduate level. Hence, it sticks most of the time to the example of the split general linear group, and, in particular, to GL₂. Main results concerning analytic properties of Eisenstein series are considered in that case. The course covers also the Langlands-Shahidi method for normalization of interwining operators, as well as the application of Eisenstein series to the spectral decomposition.