## Algebra & Number Theory

### Families of nearly ordinary Eisenstein series on unitary groups

Xin Wan

#### Abstract

We use the doubling method to construct $p$-adic $L$-functions and families of nearly ordinary Klingen Eisenstein series from nearly ordinary cusp forms on unitary groups of signature $(r,s)$ and Hecke characters, and prove the constant terms of these Eisenstein series are divisible by the $p$-adic $L$-function, following earlier constructions of Eischen, Harris, Li, Skinner and Urban. We also make preliminary computations for the Fourier–Jacobi coefficients of the Eisenstein series. This provides a framework to do Iwasawa theory for cusp forms on unitary groups.

#### Article information

Source
Algebra Number Theory, Volume 9, Number 9 (2015), 1955-2054.

Dates
Revised: 27 June 2015
Accepted: 18 August 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.ant/1510842420

Digital Object Identifier
doi:10.2140/ant.2015.9.1955

Mathematical Reviews number (MathSciNet)
MR3435811

Zentralblatt MATH identifier
1334.11083

Subjects
Primary: 11R23: Iwasawa theory

#### Citation

Wan, Xin. Families of nearly ordinary Eisenstein series on unitary groups. Algebra Number Theory 9 (2015), no. 9, 1955--2054. doi:10.2140/ant.2015.9.1955. https://projecteuclid.org/euclid.ant/1510842420

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