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 \(\varTheta\) on q-expansions and show that the algebra of Siegel modular forms mod p is stable under \({\varTheta}\), by exploiting the relation between \({\varTheta}\) and generalized Rankin-Cohen brackets.
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Böcherer, S., Nagaoka, S. On mod p properties of Siegel modular forms. Math. Ann. 338, 421–433 (2007). https://doi.org/10.1007/s00208-007-0081-7
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DOI: https://doi.org/10.1007/s00208-007-0081-7