I am particularly interested in the comparison of the trace formula part of Jacquet-Langlands. But I found the original text hard to read.
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1$\begingroup$ Take a look at Jacquet and Gelbart article in Corvallis. They give a very nice account of the trace formula part of Jacquet-Langlands. $\endgroup$– VenkataramanaCommented Feb 16, 2013 at 2:02
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3$\begingroup$ A nice summary of the Jacquet-Langlands Lecture Notes, is Alain Robert 's Bourbaki seminar archive.numdam.org/ARCHIVE/SB/SB_1971-1972__14_/… $\endgroup$– Alain ValetteCommented Feb 16, 2013 at 22:58
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1$\begingroup$ How about Gelbart's book "Automorphic Forms on Adele Groups"? Especially section 10 where he explains the comparison of the trace formulas. $\endgroup$– Judith LudwigCommented Feb 22, 2013 at 10:15
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2 Answers
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I think that you may like the notes by Ioan Badulescu: see http://www-math.univ-poitiers.fr/~badulesc/pub/JLtata1.pdf
They are a 20 pages modern essentially complete exposition of the proof of Jacquet-Langlands not only for $Gl_2$ but for higher higher rank linear groups and their inner form as well.
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1$\begingroup$ @Joel: thanks for the notes. I am at the Tata Institute but I did not know about them! I looked through the notes. They treat only the local correspondence; not the global one. I believe that most of the last chapter of Jacquet-Langlands is about the $global$ correspondence. Of course, the "local" statement uses some global ideas, but I think these notes do not treat completely the global case. $\endgroup$ Commented Feb 17, 2013 at 5:19
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I suggest Gelbart Lecture notes Arthur trace formula in addition to Gelbart Jacquet (Aakumadula`s reference).
Here is a site with references: http://www.charlesli.org/math/trace.html
answered Feb 16, 2013 at 11:23
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$\begingroup$ The LN only treat the number field case though, where as JL consider arbitrary global fields. $\endgroup$ Commented Jul 3, 2013 at 12:10