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Forum Mathematicum

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Volume 24, Issue 6

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Regularized theta lift and formulas of Katok–Sarnak type

Roland Matthes / Yoshinori Mizuno
  • Faculty and School of Engineering, The University of Tokushima, 2-1 Minami-josanjima-cho, Tokushima, 770-8506, Japan
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Published Online: 2012-11-03 | DOI: https://doi.org/10.1515/form.2011.103

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

About the article

Received: 2009-09-03

Revised: 2011-01-05

Published Online: 2012-11-03

Published in Print: 2012-11-01


Citation Information: , Volume 24, Issue 6, Pages 1239–1267, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.103.

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Citing Articles

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[1]
Roland Matthes
International Journal of Number Theory, 2017, Volume 13, Number 07, Page 1679
[2]
Roland Matthes
Journal of Number Theory, 2013, Volume 133, Number 1, Page 20

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