On the Spezialschar of Maass

Bernhard Heim

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-15

Abstract:

Let ð ‘€ 𠑘 ( ð ‘› ) be the space of Siegel modular forms of degree ð ‘› and even weight 𠑘 . In this paper firstly a certain subspace Spez ( ð ‘€ 𠑘 ( 2 ð ‘› ) ) , the Spezialschar of ð ‘€ 𠑘 ( 2 ð ‘› ) , is introduced. In the setting of the Siegel threefold, it is proven that this Spezialschar is the Maass Spezialschar. Secondly, an embedding of ð ‘€ 𠑘 ( 2 ) into a direct sum ⨠⌊ 𠑘 / 1 0 ⌋ ð œ = 0 Sym 2 ð ‘€ 𠑘 + 2 ð œ 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.

Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2010/726549.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2010/726549.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:726549

DOI: 10.1155/2010/726549

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().