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.
| Original language | English |
|---|---|
| Pages (from-to) | 1829-1878 |
| Number of pages | 50 |
| Journal | Algebra and Number Theory |
| Volume | 13 |
| Issue number | 8 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019, Mathematical Sciences Publishers. All rights reserved.
Keywords
- Shimura variety
- modular form
- theta operator