p-adic Eisenstein series and L-functions of certain cusp forms on definite unitary groups

TL;DR

This paper constructs p-adic families of Eisenstein series and L-functions for cusp forms on definite unitary groups, revealing divisibility properties related to p-adic L-functions when r=2.

Contribution

It introduces a novel construction of p-adic Eisenstein series and L-functions for non-ordinary cusp forms on definite unitary groups, expanding the scope of p-adic automorphic forms.

Findings

Constant term of Eisenstein family divisible by p-adic L-function when r=2

Construction valid for arbitrary positive r

Applicable to cusp forms unramified at p

Abstract

We construct p-adic families of Klingen Eisenstein series and L-functions for cuspforms (not necessarily ordinary) unramified at an odd prime p on definite unitary groups of signature (r, 0) (for any positive integer r) for a quadratic imaginary field split at p. When r=2, we show that the constant term of the Klingen Eisenstein family is divisible by a certain p-adic L-function.