On the analytic properties of intertwining operators I‎: ‎global normalizing factors

Document Type : Special Issue of BIMS in Honor of Professor Freydoon Shahidi



‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $\operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key ingredient in the analysis of the spectral side of Arthur's trace formula‎. ‎In particular‎, ‎it is applicable to the limit multiplicity problem studied by the authors in earlier papers‎.