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The Singular Representations
The Matrix Coefficients
The Scattering Matrix
2 other sections not shown
abelian action analytic number theory Artin asymptotics automorphic basis elements central class closed geodesics compute congruence representation conjugacy class continuous spectrum Corollary decomposes defines a representation definition degree of singularity denote depend dimension dimensional representation dimensional vector space direct sum Dirichlet series double cosets eigenvalues equivalent to jt explicit form fixed Fourier transform Frobenius reciprocity func functional equation g mod Gauss sum group G hyperbolic indB induced representation Induction-restriction irreducible components irreducible representations J(jt L-functions Maass wave forms matrix coefficients Mellin transform mod q monomial multiplicity nontrivial notation of chapter o(oo Poisson summation prime level Proof quadratic character representation of G resB root of unity scattering determinant scattering matrix Selberg zeta function singular representations space of wave square free square free level Suppose tensor product tion trace formula trivial representation unitary vector space vector valued Vigneras Weyl estimate zero estimate