Spectral Theory of Eisenstein Series Spring 2021

There is also Discord channel for the course.

The zoom link and a Discord invitation were sent to registered participants on Feb 22. Please email me if you did not receive these but would like them.

• typed notes. last update: <2021-04-20 Tue 08:52>
• handwritten notes: 1 2 3 4 5 6 7 8 9 10 11 12

We plan to discuss the basic spectral theory of automorphic forms, starting with the simplest cases, and emphasizing the role played by Eisenstein series in constructing the continuous spectrum. This book review provides an overview of the main themes.

Some familiarity with Lie groups and functional analysis.

Students wishing to receive formal credit will be encouraged to write a short paper on a topic of interest related to the course, chosen in consultation with me. I will suggest topics and be happy to discuss them with interested students. The submission deadline will be the end of June.

On the ETH network or VPN, you can access these references electronically by following the links and clicking on "Book."

• Automorphic forms on SL₂(R), Borel
• Spectral methods of automorphic forms, Iwaniec
• Some applications of modular forms, Sarnak
• A course in arithmetic, Serre (see the final chapter)
• An Introduction to Automorphic Representations with a view toward Trace Formulae, Getz and Hahn
• Automorphic forms and representations, Bump
• Spectral decomposition and Eisenstein series, Moeglin and Waldspurger
• Representation theory and automorphic functions, Gelfand, Graev and Piatetski-Shapiro
• Eisenstein series and the trace formula, Arthur