I'd like to learn about Eisenstein series so I started reading "On the Functional Equations Satisfied by Eisenstein Series"by Langlands. http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/Eisenstein-ps.pdf I'd like to go through the first few chapters.

I'm struggling already at Chapter 2 (where he goes through the background material basically) because I don't have enough Lie groups/Lie algebra background; at least this is what I think is the reason, I have only seen Lie algebra material over $\mathbb{C}$ and in the book it seems to work with some other field (I think $\mathbb{R}$) and stuff looks some what different...

I was wondering if someone who knows this book could possibly recommend me an alternative (perhaps easier) reference to study similar material or possibly a reference to cover prerequisite to go through this book. Any comments/suggestions would be appreciated. Thank you very much.

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    $\begingroup$ Asking on MO is the best way to obtain the opposite of what you want : abstract theoretical expositions lacking of the simplest relevant examples. Did you look at Garrett's website. For the $GL(\Bbb{A_Q})$ stuffs the first step is to define Dirichlet characters as characters of $GL_1(\Bbb{Q})\setminus GL_1(\Bbb{A_Q})$ and their L-functions as integrals $\endgroup$
    – reuns
    Mar 20 '19 at 20:02
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    $\begingroup$ What do you already know about Eisenstein series, and what is it that you want to learn? Are you already familiar with the classical holomorphic Eisenstein series that you find in introductory books on modular forms, such as Stein or Diamond + Shurman, for example? $\endgroup$ Mar 21 '19 at 6:49

Professor Paul Garrett's book


treats many cases treated in Langlands' book although the comparison between them will not be easy. Also, Godement's Bourbaki article deals with it.


I have heard Moeglin-Waldspurger's book is easier than Langlands' and does the same thing but I have felt it more like 'this star is nearer than that star'... I cannot reach either of them.


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