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I'm interested in reading Gelbart's book "Automorphic Forms on Adele Groups". I have a solid background knowledge at the first-year graduate level (I've passed quals), but I don't know what the prerequisites for Gelbart's book are. I've browsed through the book.

To be a bit more descriptive about my background:

  • I haven't taken a course in representation theory (beyond representations of finite groups) and would be interested in knowing where I can get the required representation theory background before reading the book.

  • In addition, I am unfamiliar with terms like the "spectrum" of the space of cusp forms, for instance.

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There are the lecture notes "AN INTRODUCTION TO AUTOMORPHIC REPRESENTATIONS" by Jayce R. Getz, which start on the background on adele rings, then treat algebraic groups and automorphic representations, Nonarchimedian Hecke algebras, a bit of archimedian representation theory, before in chapter $6$ it comes to automorphic forms on adele groups. This seems quite appropriate. For the cuspidal spectrum see [Don82] of the references, too.

The link is as follows: http://www.math.duke.edu/~jgetz/aut_reps.pdf

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