A p-adic Eisenstein measure for vector-weight automorphic forms

TL;DR

This paper constructs a p-adic Eisenstein measure for vector-weight automorphic forms on unitary groups, enabling p-adic interpolation of special automorphic form values and extending to Siegel and Hilbert modular forms.

Contribution

It introduces a new p-adic Eisenstein measure for vector-weight automorphic forms, expanding the tools for p-adic interpolation and generalizing previous constructions.

Findings

Constructed a p-adic Eisenstein measure for vector-weight automorphic forms

Enabled p-adic interpolation of special automorphic form values

Extended methods to Siegel and Hilbert modular forms

Abstract

We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C-infinity automorphic forms, including Eisenstein series, as their weights vary. We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz's p-adic families of Eisenstein series for Hilbert modular forms.