Abstract
Let G be the semidirect product A1 ∝ A of the adeles and the norm 1 ideles of a global field κ. Let Γ be the discrete subgroup κ×∝ κ. In this paper the trace formula for this setting is established and used to give the complete decomposition of the G-representation on L2(Γ\\G). It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those consists of one irreducible representation.
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