On mod p properties of Siegel modular forms

Author: Böcherer Siegfried  

Publisher: Springer Publishing Company

ISSN: 0025-5831

Source: Mathematische Annalen, Vol.338, Iss.2, 2007-06, pp. : 421-433

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Abstract

We prove two results on mod p properties of Siegel modular forms. First, we use theta series in order to construct of a Siegel modular form of weight p−1 which is congruent to 1 mod p. Second, we define a theta operator on q-expansions and show that the algebra of Siegel modular forms mod p is stable under , by exploiting the relation between and generalized Rankin-Cohen brackets.