On a certain distribution on GL(n) and explicit formulas (Q1109067)

This paper generalizes a result of \textit{A. Weil} [Izv. Akad. Nauk SSSR, Ser. Mat. 36, 3-18 (1972; Zbl 0245.12010)]. Weil's result expresses the contribution to a certain contour integral arising from the zeros of L- functions by a distribution on the Weil group. The author's idea is to define an analogous distribution on GL(n), in order to calculate the residues for the L-functions associated to cuspidal automorphic representations of the adèle group GL(n,A). The proof that these distributions do give the residues is carried out for \(n=2\), and explained for \(n>2\), modulo a conjecture. The author also observes that if \(m>n\) the distribution on GL(m) is the image of the one on GL(n) under the map induced by the natural inclusion.