A $\Lambda$-adic Kudla lift

TL;DR

This paper constructs a $p$-adic family of Picard modular forms that interpolates a Kudla lift, extending classical automorphic forms to a $p$-adic analytic setting and providing explicit formulas for Fourier-Jacobi coefficients.

Contribution

It introduces an explicit $p$-adic analytic family of Picard modular forms that interpolates the Kudla lift at various weights and levels, using Fourier-Jacobi coefficient formulas.

Findings

Constructed a $p$-adic family of Picard modular forms.

Interpolates the Kudla lift at arithmetic weights.

Provides explicit Fourier-Jacobi coefficient formulas.

Abstract

The Kudla lift studied in this article is a classical version for Picard modular forms of the automorphic theta lift between $\text{GU}(2)$ and $\text{GU}(3)$. We construct an explicit $p$-adic analytic family of Picard modular forms varying with respect to the weight and level, which interpolates a so-called $p$-modification of the lift at arithmetic weights, by exploiting a formula of Finis for the Fourier-Jacobi coefficients of a lifted form.