Showing a limited preview of this publication:
Abstract.
We study theta lifts for 
.
The theta-lift is realized via an integral transform with a Siegel theta series as kernel function.
Since this Siegel theta series fails to be square integrable, it has to be regularized. The regularization is obtained
by applying a suitable differential operator built from the Laplacian.
For the regularized theta series we compute the theta lift for cusp forms.
The regularized lift also gives a correspondence for non-cusp forms such as Eisenstein series.
Also we obtain the spectral
expansion of the theta series in either of its variables.
As an application we prove a three dimensional analogue of Katok–Sarnak's correspondence using the Selberg transform.
Keywords: Regularized theta lift; Siegel theta series; Katok–Sarnak formulas; spectral expansion of theta series
Received: 2009-09-03
Revised: 2011-01-05
Published Online: 2012-11-03
Published in Print: 2012-11-01
© 2012 by Walter de Gruyter Berlin Boston
