Eisenstein Series on Metaplectic Covers and Multiple Dirichlet Series

TL;DR

This paper computes the first Whittaker coefficient of Eisenstein series on metaplectic groups, linking it to multiple Dirichlet series and confirming a conjecture in the field.

Contribution

It establishes a connection between Eisenstein series on metaplectic covers and Weyl group multiple Dirichlet series, confirming a key conjecture.

Findings

First Whittaker coefficient computed for certain Eisenstein series

Confirmed conjecture relating metaplectic Eisenstein series to multiple Dirichlet series

Provides new insights into the structure of automorphic forms on metaplectic groups

Abstract

We computed the first Whittaker coefficient of an Eisenstein series on a global metaplectic group induced from the torus and related the result with a Weyl group multiple Dirichlet series attached to the (dual) root system of the group under a mild assumption on the root system and the degree of the metaplectic cover. This confirms a conjecture of Brubaker-Bump-Friedberg.