On the Spezialschar of Maass

2008/01/11 by Bernhard Heim, Heim, Bernhard · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #F11 #FOS: Mathematics #Number Theory (math.NT) #math.CV #math.NT #msc:F11

paper · pdf · doi:10.48550/arxiv.0801.1804

arxiv created 2008/01/11 · openalex publication_date 2008/01/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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⁽²ⁿ⁾) the Spezialschar of M_k⁽²ⁿ⁾ is introduced. In the setting of the Siegel three-fold it is proven that this Spezialschar is the Maass Spezialschar. Secondly an embedding of M_k⁽²⁾ into a direct sum ⊕_{ν= 0}^{\lfloor (k)/(10) \rfloor} Sym² M_{k + 2 ν} is given. This leads to a basic characterization of the Spezialschar property. The results of this paper are directly related to the non-vanishing of certain special values of L-functions related to the Gross-Prasad conjecture. This is illustrated by a significant example in the paper.

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• Symmetries for Siegel Theta Functions, Borcherds Lifts and Automorphic Green Functions

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