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de Shalit, Ehud; Goren, Eyal Z.

Theta operators on unitary Shimura varieties. (English) Zbl 1466.11040

Algebra Number Theory 13, No. 8, 1829-1877 (2019).
Summary: We define a theta operator on \(p\)-adic vector-valued modular forms on unitary groups of arbitrary signature, over a quadratic imaginary field in which \(p\) is inert. We study its effect on Fourier-Jacobi expansions and prove that it extends holomorphically beyond the \(\mu\)-ordinary locus, when applied to scalar-valued forms.

Cited in 1 Review
Cited in 3 Documents

MSC:

11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties

Keywords:

Shimura variety; theta operator; modular form
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\textit{E. de Shalit} and \textit{E. Z. Goren}, Algebra Number Theory 13, No. 8, 1829--1877 (2019; Zbl 1466.11040)
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