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Base change trace identity for U(3). (English) Zbl 0684.10027

The purpose of this paper is to develop a technique for comparing the Selberg trace formulae for two different groups by explaining it in the case of the author’s theory of base change for U(3). The basic form of the trace formula is not invariant under conjugation but the most significant terms for applications are. The author uses the basic form of the trace formula for the groups to be compared and a suitable definition of matching functions to deduce the trace formula in a form suitable for comparison arguments by using formal properties of the distributions involved. This then avoids Arthur’s invariant form of the trace formula and does not express either “side” of the trace formula in terms of geometric “orbital integrals” and hence avoids the finer analysis of these.
Reviewer: S.J.Patterson

MSC:

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