Spectral Multiplicity for Gl n (R)

Abstract

We study the behavior of the cuspidal spectrum of T\^, where %? is associated to Gln(i?) and V is cofinite but not compact. By a technique that modifies the Lax-Phillips technique and uses ideas from wave equation techniques, if r is the dimension of JP, Na{k) is the counting function for the Laplacian attached to a Hilbert space Ha, Ma(X) is the multiplicity function, and Ho is the space of cusp forms, we obtain the following results: Theorem 1. There exists a space of functions //' , containing all cusp forms, such that N'{X) = Cr(Vol^)AI -fC^A^A^logA)-').