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Regularized theta lift and formulas of Katok–Sarnak type
-
Roland Matthes
und
Yoshinori Mizuno
Veröffentlicht/Copyright:
3. November 2012
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
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Artikel in diesem Heft
- Masthead
- Generalized pseudohermitian manifolds
- Loop space homology associated with the mod 2 Dickson invariants
- Interacting superprocesses with discontinuous spatial motion
- Jacobsthal identity for
- Regularized theta lift and formulas of Katok–Sarnak type
- Holomorphic extensions associated with series expansions
- Stone duality for real-valued multisets
- Corrigendum: Some characterizations of finite groups in which semipermutability is a transitive relation [Forum Math.22 (2010), 855–862]
Schlagwörter für diesen Artikel
Regularized theta lift;
Siegel theta series;
Katok–Sarnak formulas;
spectral expansion of theta series
Artikel in diesem Heft
- Masthead
- Generalized pseudohermitian manifolds
- Loop space homology associated with the mod 2 Dickson invariants
- Interacting superprocesses with discontinuous spatial motion
- Jacobsthal identity for
- Regularized theta lift and formulas of Katok–Sarnak type
- Holomorphic extensions associated with series expansions
- Stone duality for real-valued multisets
- Corrigendum: Some characterizations of finite groups in which semipermutability is a transitive relation [Forum Math.22 (2010), 855–862]
