Results on a Strong Multiplicity One Theorem

Abstract

We prove an analogue of the strong multiplicity one theorem in the context of $\ddot{I}{„}_n$-spherical representations of the group $G=SO(2,1{)}^{\circ }$ appearing in $L^2(\hat{I}{“}_i\backslash G)$ for uniform torsion-free lattices $\hat{I}{“}_i,i=1,2$ in $G$. This is a generalisation of a previous result by the first author and C. S. Rajan in \cite{B-R-2011} for the case of $G=SO(2,1{)}^{\circ }$.

11 pages, accepted for publication in New York Journal of Mathematics