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We evaluate the Selberg trace formula for all discrete, irreducible, cofinite subgroups of PSL₂ ([double-struck capital]R)[italic superscript]n. In particular, this involves studying the spectral theory of the fundamental domain, and the analysis of the appropriate Eisenstein se…
In this memoir, we lay the foundations for the study of inner product formulae, one of the key technical preliminaries in the derivation of the Selberg trace formula.