Algebra & Number Theory
- Algebra Number Theory
- Volume 13, Number 8 (2019), 1829-1877.
Theta operators on unitary Shimura varieties
We define a theta operator on -adic vector-valued modular forms on unitary groups of arbitrary signature, over a quadratic imaginary field in which is inert. We study its effect on Fourier–Jacobi expansions and prove that it extends holomorphically beyond the -ordinary locus, when applied to scalar-valued forms.
Algebra Number Theory, Volume 13, Number 8 (2019), 1829-1877.
Received: 1 January 2018
Revised: 9 January 2019
Accepted: 13 June 2019
First available in Project Euclid: 29 October 2019
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de Shalit, Ehud; Goren, Eyal Z. Theta operators on unitary Shimura varieties. Algebra Number Theory 13 (2019), no. 8, 1829--1877. doi:10.2140/ant.2019.13.1829. https://projecteuclid.org/euclid.ant/1572314506