Results on a Strong Multiplicity One Theorem

TL;DR

This paper establishes a strong multiplicity one theorem for certain spherical representations of the group SO(2,1) in the context of uniform torsion-free lattices, extending previous results to a broader setting.

Contribution

It generalizes a prior multiplicity one theorem to the setting of $ au_n$-spherical representations of SO(2,1), broadening the scope of the original result.

Findings

Proves an analogue of the strong multiplicity one theorem for SO(2,1)

Extends previous results to $ au_n$-spherical representations

Applicable to uniform torsion-free lattices in the group

Abstract

We prove an analogue of the strong multiplicity one theorem in the context of $\tau_n$-spherical representations of the group $G = SO(2,1)^\circ$ appearing in $L^2(\Gamma_i \backslash G)$ for uniform torsion-free lattices $\Gamma_i, i = 1, 2$ 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 $G = SO(2,1)^\circ$.