Abstract
For a Siegel modular cusp formf of weightk letv(f) be the closure of the convex ray hull of the support of the Fourier series inside the cone of semidefinite forms. We show the existence of the extreme core,C ext, which satisfiesv(f) ⊇k Cext for all cusp forms. This is a generalization of the Valence Inequality to Siegel modular cusp forms. We give estimations of the extreme core for general n. For n ≤5 we use noble forms to improve these estimates. Forn = 2 we almost specify the extreme core but fall short. We supply improved estimates for all relevant constants and show optimality in some cases. The techniques are mainly from the geometry of numbers but we also use IGUSA’s generators for the ring of Siegel modular forms in degree two.
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R. Berndt
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Poor, C., Yuen, D.S. The extreme core. Abh.Math.Semin.Univ.Hambg. 75, 51–75 (2005). https://doi.org/10.1007/BF02942035
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DOI: https://doi.org/10.1007/BF02942035