International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 726549, 15 pages
Research Article

On the Spezialschar of Maass

German University of Technology in Oman, Way no. 36, Building no. 331, North Ghubrah, Muscat, Oman

Received 28 July 2010; Accepted 27 October 2010

Academic Editor: Aloys Krieg

Copyright © 2010 Bernhard Heim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 𝑀 𝑘 ( 𝑛 ) be the space of Siegel modular forms of degree 𝑛 and even weight 𝑘 . In this paper firstly a certain subspace Spez ( 𝑀 𝑘 ( 2 𝑛 ) ) , the Spezialschar of 𝑀 𝑘 ( 2 𝑛 ) , is introduced. In the setting of the Siegel threefold, it is proven that this Spezialschar is the Maass Spezialschar. Secondly, an embedding of 𝑀 𝑘 ( 2 ) into a direct sum 𝑘 / 1 0 𝜐 = 0 Sym2 𝑀 𝑘 + 2 𝜐 is given. This leads to a basic characterization of the Spezialschar property. The results of this paper are directly related to the nonvanishing of certain special values of L-functions related to the Gross-Prasad conjecture. This is illustrated by a significant example in the paper.