On the Spezialschar of Maass | Zendy

Bernhard Heim | Zendy

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On the Spezialschar of Maass

Author(s) -

Bernhard Heim

Publication year - 2010

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2010/726549

Subject(s) - mathematics , siegel modular form , conjecture , embedding , subspace topology , pure mathematics , property (philosophy) , modular form , space (punctuation) , degree (music) , algebra over a field , mathematical analysis , epistemology , philosophy , linguistics , physics , artificial intelligence , computer science , acoustics

Let () be the space of Siegel modular forms of degree and even weight . In this paper firstly a certain subspace Spez((2)), the Spezialschar of (2), is introduced. In the setting of the Siegel threefold, it is proven that this Spezialschar is the Maass Spezialschar. Secondly, an embedding of (2) into a direct sum ⨁⌊/10⌋=0 Sym2+2 is given. This leads to a basic characterization of the Spezialschar property. Theresults of this paper are directly related to the nonvanishing of certainspecial values of L-functions related to the Gross-Prasad conjecture. Thisis illustrated by a significant example in the paper

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