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Stable trace formula: Cuspidal tempered terms. (English) Zbl 0576.22020
Let G be a reductive group over a number field F. The meaning and the importance of a ”stable” trace formula for G are explained by R. P. Langlands in ”Les débuts d’une formule des traces stable” [Publ. Math. Univ. Paris VII, 13 (1983; Zbl 0532.22017)]. There he gives explicitly the stabilization of the regular elliptic part of the trace formula. In particular, he defines, for any elliptic endoscopic group H of G, a number \(\iota\) (G,H) relating the stable trace formula for H to the trace formula for G. In the present paper the author proves an identity for \(\iota\) (G,H) involving Tamagawa numbers. He uses this expression for \(\iota\) (G,H) in a ”speculative” consideration concerning the tempered cuspidal part of the trace formula and its stabilization.
Reviewer: J.G.M.Mars

MSC:
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
11F70 Representation-theoretic methods; automorphic representations over local and global fields
12G05 Galois cohomology
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