On a spectral analogue of the strong multiplicity one theorem

Bhagwat, Chandrasheel ; Rajan, C. S. (2010) On a spectral analogue of the strong multiplicity one theorem International Mathematics Research Notices, 18 . pp. 4059-4073. ISSN 1073-7928

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Official URL: http://imrn.oxfordjournals.org/content/2011/18/405...

Related URL: http://dx.doi.org/10.1093/imrn/rnq243

Abstract

We prove spectral analogues of the classical strong multiplicity one theorem for newforms. Let Γ1 and Γ2 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 L21\G) and L22\G). Then L21\G)≅L22/G) as G - modules (resp. the spherical spectra of L21\G) and L22\G) are equal).

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