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Oct 13, 2020 at 2:06 comment added Peter Humphries This question is somewhat answered in a paper of Arthur: doi.org/10.1215/S0012-7094-82-04904-3. There is a Maass-Selberg identity stated at the beginning of Section 9; in general, this can be quite complicated, and Arthur's main goal is just to understand the asymptotics of this as the truncation parameter $T$ tends to infinity. But I imagine for $G = \mathrm{GL}_n$, one could actually make this reasonably explicit.
Sep 26, 2020 at 9:45 history asked Subhajit Jana CC BY-SA 4.0