Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2017: 0.695
5-year IMPACT FACTOR: 0.750

CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 0.966
Source Normalized Impact per Paper (SNIP) 2017: 0.889

Mathematical Citation Quotient (MCQ) 2016: 0.75

See all formats and pricing
More options …
Volume 24, Issue 6


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
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2012-11-03 | DOI: https://doi.org/10.1515/form.2011.103


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.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

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

Comments (0)

Please log in or register to comment.
Log in