Metaplectic Eisenstein Distributions

TL;DR

This paper introduces distributional analogues of metaplectic Eisenstein series for SL(2,R), proving their meromorphic continuation and functional equations, which lead to new insights into classical metaplectic Eisenstein series.

Contribution

It defines metaplectic Eisenstein distributions and establishes their meromorphic continuation and functional equations, advancing the understanding of metaplectic automorphic forms.

Findings

Distributional analogues of Eisenstein series are well-defined.

Metaplectic Eisenstein distributions have meromorphic continuation.

Functional equations for these distributions are explicitly derived.

Abstract

In this paper, we define distributional analogues of the metaplectic Eisenstein series for $\text{SL}_2(\mathbb{R})$, which we refer to as metaplectic Eisenstein distributions. We prove that these distributions have meromorphic continuation and give an explicit functional equation that they satisfy. From these results, we deduce the functional equation for the corresponding classical metaplectic Eisenstein series.