On a family of distributions obtained from Eisenstein series. II: Explicit formulas. (English) Zbl 0562.22004

Arthur, James

Am. J. Math. 104, 1289-1336 (1982).

The goal is to obtain an explicit formula for the Eisenstein series terms in the trace formula for a reductive group over \(\mathbb Q\). The reader must have read the author’s previous papers on the subject to understand the problem and solution. The main results include a formula for Arthur’s truncation polynomials. The first version of such a formula has defects; e.g. it contains a test function and a limit. The second half of the paper attempts to eliminate this and is based on the assumption that the intertwining operators between induced representations on the local groups can all be suitably normalized. At the time of this paper canonical normalizations had only been found for \(\mathrm{GL}(n)\).
[Part I, cf. ibid. 104, 1243–1288 (1982; Zbl 0541.22010)].

Reviewer: Audrey A. Terras (La Jolla)

MSC:

22E55	Representations of Lie and linear algebraic groups over global fields and adèle rings
11F72	Spectral theory; trace formulas (e.g., that of Selberg)
43A80	Analysis on other specific Lie groups
11F70	Representation-theoretic methods; automorphic representations over local and global fields
22E30	Analysis on real and complex Lie groups

Keywords:

Eisenstein series; trace formula; reductive group; truncation polynomials

Citations:

Zbl 0541.22010