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

Abstract

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 $GL(n)$; 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.

To Freydoon Shahidi, for his upcoming 70th birthday

References in corpus (2)

• Dual R-groups of the inner forms of SL(N)
• Comparaison des paramètres de Langlands et des exposants à l'intérieur d'un paquet d'Arthur

Cited by in corpus (3)

• On the remainder term of the Weyl law for congruence subgroups of Chevalley groups
• Analytic torsion of arithmetic quotients of the symmetric space SL(n,R)/SO(n)
• Approximation of $L^2$-analytic torsion for arithmetic quotients of the symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$