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Apr 7, 2014 at 14:45 comment added Marc Palm Note that my computation apply only to the highest type. For the computations at the real places and the unramified complex cases, you can have a look at my PhD thesis. There is a good reason for working with highest types/smallest weights = irreducible $K$-reps as soon as you have pinned down the local conditions.
Apr 7, 2014 at 14:38 comment added Tian An Thanks! Especially for pointing out that the functional equation gives a straightforward interpretation of $M(s)^{-1}$. I am trying to compute the $M(s)$ explicitly in certain cases and am stuck with some computations. I will look through your computations and see if it can help me.
Apr 7, 2014 at 14:35 vote accept Tian An
Mar 29, 2014 at 22:29 history edited Marc Palm CC BY-SA 3.0
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Mar 29, 2014 at 20:57 history edited Marc Palm CC BY-SA 3.0
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Mar 29, 2014 at 20:38 history answered Marc Palm CC BY-SA 3.0