%0 Journal Article
%T On a spectral analogue of the strong multiplicity one theorem
%A Chandrasheel Bhagwat
%A C. S. Rajan
%J Mathematics
%D 2010
%I arXiv
%X We prove spectral analogues of the classical strong multiplicity one theorem for newforms. Let $\Gamma_1$ and $\Gamma_2$ be uniform lattices in a semisimple group $G$. Suppose all but finitely many irreducible unitary representations (resp. spherical) of $G$ occur with equal multiplicities in $L^{2}(\Gamma_1 \backslash G)$ and $L^{2}(\Gamma_2 \backslash G)$. Then $L^{2}(\Gamma_1 \backslash G) \cong L^{2}(\Gamma_2 \backslash G)$ as $G$ - modules (resp. the spherical spectra of $L^{2}(\Gamma_1 \backslash G)$ and $L^{2}(\Gamma_2 \backslash G)$ are equal).
%U http://arxiv.org/abs/1009.0694v1