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 | American 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
Funding Information:Much of this paper was written during visits to the Hebrew University and to McGill University and it is our pleasant duty to thank these institutes for their hospitality. This research was supported by NSERC grant 223148 and ISF grant 276/17.
Funding Information:
We would like to thank Ellen Eischen and Elena Mantovan for discussions relating to the contents of both our papers. It is a pleasure to thank G. Rosso for bringing their work to our attention, and P. Kassaei for valuable comments. We thank the referees for very useful comments. Much of this paper was written during visits to the Hebrew University and to McGill University and it is our pleasant duty to thank these institutes for their hospitality. This research was supported by NSERC grant 223148 and ISF grant 276/17.
Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.
Keywords
- Shimura variety
- modular form
- theta operator