## Algebra & Number Theory

### Theta operators on unitary Shimura varieties

#### Abstract

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 $μ$-ordinary locus, when applied to scalar-valued forms.

#### Article information

Source
Algebra Number Theory, Volume 13, Number 8 (2019), 1829-1877.

Dates
Revised: 9 January 2019
Accepted: 13 June 2019
First available in Project Euclid: 29 October 2019

https://projecteuclid.org/euclid.ant/1572314506

Digital Object Identifier
doi:10.2140/ant.2019.13.1829

Mathematical Reviews number (MathSciNet)
MR4017536

Zentralblatt MATH identifier
07118654

#### Citation

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

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