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.

46 pages

References in corpus (3)

• Differential operators and families of automorphic forms on unitary groups of arbitrary signature
• Theta operators on Siegel modular forms and Galois representations
• Foliations on unitary Shimura varieties in positive characteristic

Cited by in corpus (7)

• Entire theta operators at unramified primes
• Differential operators mod $p$: analytic continuation and consequences
• Geometric weight-shifting operators on Hilbert modular forms in characteristic p
• Foliations on unitary Shimura varieties in positive characteristic
• Families of Differential Operators for Overconvergent Hilbert Modular Forms
• An introduction to Eisenstein measures
• Differential operators on modular forms (mod p)