Theta operators on unitary Shimura varieties

Ehud de Shalit, Eyal Z. Goren

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 languageAmerican English
Pages (from-to)1829-1878
Number of pages50
JournalAlgebra and Number Theory
Volume13
Issue number8
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.

Keywords

  • Shimura variety
  • modular form
  • theta operator

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