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I've been digging for awhile to not much success, so I figure I would try here:

I am looking for some references which compute explicitly examples of Rankin-Selberg L-functions from the constant terms of Eisenstein series (maximal and, if possible, non-maximal parabolic) attached to GL(n), for some $n>2.$

It seems that most of the references I am able to find (Shahidi, Kim, Muller, etc.) which do something of this sort do this in either for GL(2) or for general $G$.

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  • $\begingroup$ First, there are several I can point you to once I get to the department that are more recent, but there is always Cogdell's notes on $GL(n)\times GL(n)$ L-functions. Second, what do you mean "from the constant terms"? I wasn't aware the constant terms were ever involved with Rankin-Selberg calculations. $\endgroup$
    – Spencer Leslie
    Commented Jul 24, 2015 at 10:32
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    $\begingroup$ I'm thinking of Rankin-Selberg L-functions that arise as constant terms of Eisenstein series/normalizing factors of intertwining operators, i.e., Langlands-Shahidi method rather than Rankin-Selberg where you integrate two forms against an Eisenstein series. $\endgroup$
    – Tian An
    Commented Jul 24, 2015 at 14:32
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    $\begingroup$ Maybe you should rephrase the question to be about the Langlands-Shahidi method for clarity. From the title, it sounds like you're asking for things like the $GL(n) \times GL(n)$ Rankin-Selberg method. $\endgroup$
    – Kimball
    Commented Aug 10, 2015 at 5:44

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